Circle

105 questions · Mathematics · JEE Main

Circle

105 questions · Mathematics · JEE Main

The absolute difference between the squares of the radii of the two circles passing through the point $(- 9, 4)$ and touching the lines $x + y = 3$ and $x - y = 3$ , is equal to .2025 · 2 Apr · Shift 1 · Q49 · Numerical
If the four distinct points $(4, 6), (- 1, 5), (0, 0)$ and $(k, 3 k)$ lie on a circle of radius $r$ , then $10 k + r^{2}$ is equal to2025 · 3 Apr · Shift 2 · Q45 · MCQ
Let $C$ be the circle $x^{2} + (y - 1)^{2} = 2, E_{1}$ and $E_{2}$ be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line $x + y = 3$ touch the curves $C, E_{1}$ and $E_{2}$ at $P (x_{1}, y_{1}), Q (x_{2}, y_{2})$ …2025 · 4 Apr · Shift 1 · Q46 · Numerical
Let $C_{1}$ be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let $C_{2}$ be the circle with centre $(1, 3)$ that touches $C_{1}$ externally at the point $(α, β)$ . If $(β - α)^{2} = \frac{m}{n}$ …2025 · 7 Apr · Shift 1 · Q27 · MCQ
A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point $(2, 5)$ and intersects the circle $C$ at exactly two points. If the set of all possible…2025 · 22 Jan · Shift 1 · Q33 · MCQ
Let the circle $C$ touch the line $x - y + 1 = 0$ , have the centre on the positive $x$ -axis, and cut off a chord of length $\frac{4}{13}$ along the line $- 3 x + 2 y = 1$ . Let H be the hyperbola $\frac{x ^{2}}{α ^{2}} - \frac{y ^{2}}{β ^{2}} = 1$ ,…2025 · 23 Jan · Shift 1 · Q49 · Numerical
Let circle $C$ be the image of $x^{2} + y^{2} - 2 x + 4 y - 4 = 0$ in the line $2 x - 3 y + 5 = 0$ and $A$ be the point on $C$ such that $O A$ is parallel to $x$ -axis and $A$ lies on the right hand side of the centre $O$ of $C$ . If $B (α, β)$ , with $β < 4$ …2025 · 24 Jan · Shift 1 · Q45 · MCQ
Let the equation of the circle, which touches $x$ -axis at the point $(a, 0), a > 0$ and cuts off an intercept of length $b$ on $y - a x i s$ be $x^{2} + y^{2} - α x + β y + γ = 0$ . If the circle lies below $x - a x i s$ , then the ordered pair…2025 · 28 Jan · Shift 1 · Q42 · MCQ
Let the line x+y=1 meet the circle $x^{2} + y^{2} = 4$ at the points A and B. If the line perpendicular to AB and passing through the mid-point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ABCD is equal to :2025 · 29 Jan · Shift 1 · Q42 · MCQ
Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on 3x + 2y + 2 = 0. Then the length of the chord, of the circle C, whose mid-point is (1, 2), is:2025 · 29 Jan · Shift 2 · Q37 · MCQ
Let $C : x^{2} + y^{2} = 4$ and $C^{'} : x^{2} + y^{2} - 4 λ x + 9 = 0$ be two circles. If the set of all values of $λ$ so that the circles $C$ and $C$ intersect at two distinct points, is $\mathrm{R}-[\mathrm{a},…2024 · 1 Feb · Shift 1 · Q48 · MCQ
Let the locus of the midpoints of the chords of the circle $x^{2} + (y - 1)^{2} = 1$ drawn from the origin intersect the line $x + y = 1$ at $P$ and $Q$ . Then, the length of $PQ$ is :2024 · 1 Feb · Shift 2 · Q43 · MCQ
A square is inscribed in the circle $x^{2} + y^{2} - 10 x - 6 y + 30 = 0$ . One side of this square is parallel to $y = x + 3$ . If $(x_{i}, y_{i})$ are the vertices of the square, then $Σ (x_{i}^{2} + y_{i}^{2})$ is equal to:2024 · 4 Apr · Shift 1 · Q35 · MCQ
Let $C$ be a circle with radius $10$ units and centre at the origin. Let the line $x + y = 2$ intersects the circle $C$ at the points $P$ and $Q$ . Let $MN$ be a chord of $C$ of…2024 · 4 Apr · Shift 2 · Q44 · MCQ
Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point $(3, 2)$ and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point $(5, 5)$ is :2024 · 5 Apr · Shift 1 · Q37 · MCQ
Let the circle $C_{1} : x^{2} + y^{2} - 2 (x + y) + 1 = 0$ and $C_{2}$ be a circle having centre at $(- 1, 0)$ and radius 2 . If the line of the common chord of $C_{1}$ and $C_{2}$ intersects the $y$ -axis at the point…2024 · 5 Apr · Shift 2 · Q31 · MCQ
Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC…2024 · 5 Apr · Shift 2 · Q33 · MCQ
A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are $m$ and $n$ , respectively, then $m + n^{2}$ is equal to2024 · 6 Apr · Shift 1 · Q31 · MCQ
If $P (6, 1)$ be the orthocentre of the triangle whose vertices are $A (5, - 2), B (8, 3)$ and $C (h, k)$ , then the point $C$ lies on the circle :2024 · 6 Apr · Shift 2 · Q44 · MCQ
Let the circles $C_{1} : (x - α)^{2} + (y - β)^{2} = r_{1}^{2}$ and $C_{2} : (x - 8)^{2} + (y - \frac{15}{2})^{2} = r_{2}^{2}$ touch each other externally at the point $(6, 6)$ . If the point $(6, 6)$ divides the line segment joining the centres of the circles…2024 · 8 Apr · Shift 1 · Q35 · MCQ
If the image of the point $(- 4, 5)$ in the line $x + 2 y = 2$ lies on the circle $(x + 4)^{2} + (y - 3)^{2} = r^{2}$ , then $r$ is equal to:2024 · 8 Apr · Shift 2 · Q49 · MCQ
Let a circle passing through $(2, 0)$ have its centre at the point $(h, k)$ . Let $(x_{c}, y_{c})$ be the point of intersection of the lines $3 x + 5 y = 1$ and $(2 + c) x + 5 c^{2} y = 1$ . If $h = lim_{c \to 1} x_{c}$ …2024 · 9 Apr · Shift 1 · Q40 · MCQ
Let the centre of a circle, passing through the points $(0, 0), (1, 0)$ and touching the circle $x^{2} + y^{2} = 9$ , be $(h, k)$ . Then for all possible values of the coordinates of the centre $(h, k), 4 (h^{2} + k^{2})$ is equal to …2024 · 9 Apr · Shift 1 · Q56 · Numerical
Four distinct points $(2 k, 3 k), (1, 0), (0, 1)$ and $(0, 0)$ lie on a circle for $k$ equal to :2024 · 27 Jan · Shift 1 · Q42 · MCQ
Consider a circle $(x - α)^{2} + (y - β)^{2} = 50$ , where $α, β > 0$ . If the circle touches the line $y + x = 0$ at the point $P$ , whose distance from the origin is $42$ , then $(α + β)^{2}$ is equal to …2024 · 27 Jan · Shift 2 · Q58 · Numerical
Equations of two diameters of a circle are $2 x - 3 y = 5$ and $3 x - 4 y = 7$ . The line joining the points $(- \frac{22}{7}, - 4)$ and $(- \frac{1}{7}, 3)$ intersects the circle at only one point $P (α, β)$ . Then, $17 β - α$ …2024 · 29 Jan · Shift 1 · Q53 · Numerical
If the circles $(x + 1)^{2} + (y + 2)^{2} = r^{2}$ and $x^{2} + y^{2} - 4 x - 4 y + 4 = 0$ intersect at exactly two distinct points, then2024 · 30 Jan · Shift 1 · Q33 · MCQ
Consider two circles $C_{1} : x^{2} + y^{2} = 25$ and $C_{2} : (x - α)^{2} + y^{2} = 16$ , where $α \in (5, 9)$ . Let the angle between the two radii (one to each circle) drawn from one of the intersection points of $C_{1}$ and $C_{2}$ be $sin^{- 1} (\frac{63}{8})$ …2024 · 30 Jan · Shift 2 · Q54 · Numerical
If one of the diameters of the circle $x^{2} + y^{2} - 10 x + 4 y + 13 = 0$ is a chord of another circle $C$ , whose center is the point of intersection of the lines $2 x + 3 y = 12$ and $3 x - 2 y = 5$ , then the radius of the circle $C$ is :2024 · 31 Jan · Shift 1 · Q49 · MCQ
Let a variable line passing through the centre of the circle $x^{2} + y^{2} - 16 x - 4 y = 0$ , meet the positive co-ordinate axes at the points $A$ and $B$ . Then the minimum value of $O A + O B$ , where $O$ is the origin, is equal to2024 · 31 Jan · Shift 2 · Q48 · MCQ
Let the point $(p, p + 1)$ lie inside the region $E = {(x, y) : 3 - x \leq y \leq 9 - x^{2}, 0 \leq x \leq 3}$ . If the set of all values of $p$ is the interval $(a, b)$ , then $b^{2} + b - a^{2}$ is equal to …2023 · 6 Apr · Shift 1 · Q38 · Numerical
A circle passing through the point $P (α, β)$ in the first quadrant touches the two coordinate axes at the points $A$ and $B$ . The point $P$ is above the line $A B$ . The point $Q$ on the line segment $A B$ is the foot of…2023 · 6 Apr · Shift 1 · Q41 · Numerical
Consider a circle $C_{1} : x^{2} + y^{2} - 4 x - 2 y = α - 5$ . Let its mirror image in the line $y = 2 x + 1$ be another circle $C_{2} : 5 x^{2} + 5 y^{2} - 10 f x - 10 g y + 36 = 0$ . Let $r$ be the radius of $C_{2}$ . Then $α + r$ is equal to …2023 · 8 Apr · Shift 1 · Q46 · Numerical
A line segment AB of length $λ$ moves such that the points A and B remain on the periphery of a circle of radius $λ$ . Then the locus of the point, that divides the line segment AB in the ratio 2 : 3, is a circle of radius :2023 · 10 Apr · Shift 1 · Q35 · MCQ
Let A be the point $(1, 2)$ and B be any point on the curve $x^{2} + y^{2} = 16$ . If the centre of the locus of the point P, which divides the line segment $AB$ in the ratio $3 : 2$ is the point C $(α, β)$ , then the length of…2023 · 10 Apr · Shift 2 · Q31 · MCQ
Two circles in the first quadrant of radii $r_{1}$ and $r_{2}$ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line $x + y = 2$ . Then $r_{1}^{2} + r_{2}^{2} - r_{1} r_{2}$ is equal to .2023 · 12 Apr · Shift 1 · Q37 · Numerical
The locus of the mid points of the chords of the circle $C_{1} : (x - 4)^{2} + (y - 5)^{2} = 4$ which subtend an angle $θ_{i}$ at the centre of the circle $C_{1}$ , is a circle of radius $r_{i}$ . If $θ_{1} = \frac{π}{3}, θ_{3} = \frac{2 π}{3}$ …2023 · 24 Jan · Shift 2 · Q29 · MCQ
The points of intersection of the line $a x + b y = 0, (a e b)$ and the circle $x^{2} + y^{2} - 2 x = 0$ are $A (α, 0)$ and $B (1, β)$ . The image of the circle with AB as a diameter in the line $x + y + 2 = 0$ is :2023 · 25 Jan · Shift 1 · Q34 · MCQ
Let the tangents at the points $A (4, - 11)$ and $B (8, - 5)$ on the circle $x^{2} + y^{2} - 3 x + 10 y - 15 = 0$ , intersect at the point $C$ . Then the radius of the circle, whose centre is $C$ and the line joining $A$ and $B$ is its tangent, is equal to :2023 · 29 Jan · Shift 1 · Q27 · MCQ
Let $P (a_{1}, b_{1})$ and $Q (a_{2}, b_{2})$ be two distinct points on a circle with center $C (2, 3)$ . Let $O$ be the origin and $OC$ be perpendicular to both $CP$ and $CQ$ . If…2023 · 30 Jan · Shift 2 · Q40 · Numerical
The set of all values of $a^{2}$ for which the line $x + y = 0$ bisects two distinct chords drawn from a point $P (\frac{1 + a}{2}, \frac{1 - a}{2})$ on the circle $2 x^{2} + 2 y^{2} - (1 + a) x - (1 - a) y = 0$ , is equal to :2023 · 31 Jan · Shift 2 · Q37 · MCQ
Let a circle C : (x $-$ h)2 + (y $-$ k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to …2022 · 24 Jun · Shift 2 · Q43 · Numerical
Let the abscissae of the two points P and Q be the roots of $2 x^{2} - r x + p = 0$ and the ordinates of P and Q be the roots of $x^{2} - s x - q = 0$ . If the equation of the circle described on PQ as diameter is $2 (x^{2} + y^{2}) - 11 x - 14 y - 22 = 0$ …2022 · 25 Jun · Shift 1 · Q41 · Numerical
Let the abscissae of the two points $P$ and $Q$ on a circle be the roots of $x^{2} - 4 x - 6 = 0$ and the ordinates of $P$ and $Q$ be the roots of $y^{2} + 2 y - 7 = 0$ . If $PQ$ is a diameter of the circle $x^{2} + y^{2} + 2 a x + 2 b y + c = 0$ …2022 · 26 Jul · Shift 2 · Q29 · MCQ
If the circle $x^{2} + y^{2} - 2 g x + 6 y - 19 c = 0, g, c \in R$ passes through the point $(6, 1)$ and its centre lies on the line $x - 2 cy = 8$ , then the length of intercept made by the circle on $x$ -axis is :2022 · 27 Jul · Shift 1 · Q37 · MCQ
A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x $-$ y + 4 = 0, then the area of R is .2022 · 27 Jun · Shift 1 · Q41 · Numerical
The set of values of k, for which the circle $C : 4 x^{2} + 4 y^{2} - 12 x + 8 y + k = 0$ lies inside the fourth quadrant and the point $(1, - \frac{1}{3})$ lies on or inside the circle C, is :2022 · 27 Jun · Shift 2 · Q30 · MCQ
For $t \in (0, 2 π)$ , if $ABC$ is an equilateral triangle with vertices $A (sin t, - cos t), B (cost, sin t)$ and $C (a, b)$ such that its orthocentre lies on a circle with centre…2022 · 28 Jul · Shift 1 · Q28 · MCQ
Let $C$ be the centre of the circle $x^{2} + y^{2} - x + 2 y = \frac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $C$ , makes an angle of $\frac{π}{4}$ with the line $CP$ and intersects the circle at…2022 · 28 Jul · Shift 1 · Q32 · MCQ
If one of the diameters of the circle $x^{2} + y^{2} - 22 x - 62 y + 14 = 0$ is a chord of the circle $(x - 22)^{2} + (y - 22)^{2} = r^{2}$ , then the value of r2 is equal to .2022 · 28 Jun · Shift 2 · Q43 · Numerical
Let the mirror image of a circle $c_{1} : x^{2} + y^{2} - 2 x - 6 y + α = 0$ in line $y = x + 1$ be $c_{2} : 5 x^{2} + 5 y^{2} + 10 g x + 10 f y + 38 = 0$ . If $r$ is the radius of circle $c_{2}$ , then $α + 6 r^{2}$ is equal to …2022 · 29 Jul · Shift 1 · Q47 · Numerical
Let $A B$ be a chord of length 12 of the circle $(x - 2)^{2} + (y + 1)^{2} = \frac{169}{4}$ . If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$ , then five times the distance of point $P$ from chord $A B$ is equal to …2022 · 29 Jul · Shift 2 · Q41 · Numerical
$Let S = {(x, y) \in N \times N : 9 (x - 3)^{2} + 16 (y - 4)^{2} \leq 144}$ and $T = {(x, y) \in R \times R : (x - 7)^{2} + (y - 4)^{2} \leq 36}$ . Then $n (S \cap T)$ is equal to …2022 · 29 Jul · Shift 2 · Q43 · Numerical
Let a triangle ABC be inscribed in the circle $x^{2} - 2 (x + y) + y^{2} = 0$ such that $∠ B A C = \frac{π}{2}$ . If the length of side AB is $2$ , then the area of the $Δ$ ABC is equal to :2022 · 29 Jun · Shift 2 · Q30 · MCQ
Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2 $2$ and 2 $5$ , respectively. Then the shortest distance from origin to a tangent to this circle which is…2021 · 16 Mar · Shift 2 · Q37 · MCQ
For the four circles M, N, O and P, following four equations are given : Circle M : x2 + y2 = 1 Circle N : x2 + y2 $-$ 2x = 0 Circle O : x2 + y2 $-$ 2x $-$ 2y + 1 = 0 Circle P : x2 + y2 $-$ 2y = 0 If the centre of circle M is joined with…2021 · 18 Mar · Shift 1 · Q33 · MCQ
Let the circle S : 36x2 + 36y2 $-$ 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x $-$ 2y = 4 and 2x $-$ y = 5 lies inside the circle S, then :2021 · 22 Jul · Shift 2 · Q33 · MCQ
If one of the diameters of the circle x2 + y2 - 2x - 6y + 6 = 0 is a chord of another circle 'C', whose center is at (2, 1), then its radius is .2021 · 24 Feb · Shift 1 · Q41 · Numerical
Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point ( $-$ 5, 0). If the locus of the point P is a circle of radius r, then 4r2 is equal to 2021 · 24 Feb · Shift 2 · Q34 · Numerical
If a line along a chord of the circle 4x2 + 4y2 + 120x + 675 = 0, passes through the point ( $-$ 30, 0) and is tangent to the parabola y2 = 30x, then the length of this chord is :2021 · 26 Aug · Shift 1 · Q30 · MCQ
The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units, is a circle of diameter d. Then d2 is equal to .2021 · 26 Aug · Shift 1 · Q39 · Numerical
A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y $-$ 5 = 0 at two points P and Q such that PQ is a diameter of C1. Then the diameter of C is :2021 · 26 Aug · Shift 2 · Q37 · MCQ
In the circle given below, let OA = 1 unit, OB = 13 unit and PQ $⊥$ OB. Then, the area of the triangle PQB (in square units) is : Includes diagram2021 · 26 Feb · Shift 1 · Q31 · MCQ
Let A(1, 4) and B(1, $-$ 5) be two points. Let P be a point on the circle (x $-$ 1)2 + (y $-$ 1)2 = 1 such that (PA)2 + (PB)2 have maximum value, then the points, P, A and B lie on :2021 · 26 Feb · Shift 2 · Q27 · MCQ
If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of radius r, then r is equal to :2021 · 26 Feb · Shift 2 · Q37 · MCQ
Let Z be the set of all integers, $A = {(x, y) \in Z \times Z : (x - 2)^{2} + y^{2} \leq 4}$ $B = {(x, y) \in Z \times Z : x^{2} + y^{2} \leq 4}$ $C = {(x, y) \in Z \times Z : (x - 2)^{2} + (y - 2)^{2} \leq 4}$ If the total number of…2021 · 27 Aug · Shift 2 · Q31 · MCQ
Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :2021 · 27 Jul · Shift 1 · Q35 · MCQ
Let $A = {(x, y) \in R \times R ∣2 x^{2} + 2 y^{2} - 2 x - 2 y = 1}$ , $B = {(x, y) \in R \times R ∣4 x^{2} + 4 y^{2} - 16 y + 7 = 0}$ and $C = {(x, y) \in R \times R ∣ x^{2} + y^{2} - 4 x - 2 y + 5 \leq r^{2}}$ . Then the minimum value of |r|…2021 · 27 Jul · Shift 1 · Q38 · MCQ
Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $65$ on the x-axis. Then the radius of the circle C is equal to :2021 · 27 Jul · Shift 2 · Q36 · MCQ
If the variable line 3x + 4y = $α$ lies between the two circles (x $-$ 1)2 + (y $-$ 1)2 = 1 and (x $-$ 9)2 + (y $-$ 1)2 = 4, without intercepting a chord on either circle, then the sum of all the integral values of $α$ is …2021 · 31 Aug · Shift 1 · Q41 · Numerical
The diameter of the circle, whose centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2, is .2020 · 3 Sep · Shift 1 · Q38 · Numerical
Let PQ be a diameter of the circle x2 + y2 = 9. If $α$ and $β$ are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of $α β$ is .2020 · 4 Sep · Shift 2 · Q34 · Numerical
If the length of the chord of the circle, x2 + y2 = r2 (r > 0) along the line, y – 2x = 3 is r, then r2 is equal to :2020 · 5 Sep · Shift 2 · Q31 · MCQ
If the curves, x2 – 6x + y2 + 8 = 0 and x2 – 8y + y2 + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is .2020 · 9 Jan · Shift 2 · Q38 · Numerical
The sum of the squares of the lengths of the chords intercepted on the circle, x2 + y2 = 16, by the lines, x + y = n, n $\in$ N, where N is the set of all natural numbers, is :2019 · 8 Apr · Shift 1 · Q44 · MCQ
A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two adjacent vertices of the rectangle are (–8, 5) and (6, 5), then the area of the rectangle (in sq. units) is :2019 · 9 Apr · Shift 2 · Q30 · MCQ
If the area of an equilateral triangle inscribed in the circle x2 + y2 + 10x + 12y + c = 0 is $273$ sq units then c is equal to :2019 · 10 Jan · Shift 2 · Q44 · MCQ
The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :2019 · 11 Jan · Shift 1 · Q20 · MCQ
A square is inscribed in the circle x2 + y2 – 6x + 8y – 103 = 0 with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is :2019 · 11 Jan · Shift 1 · Q25 · MCQ
If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90o, then the length (in cm) of their common chord is :2019 · 12 Apr · Shift 1 · Q43 · MCQ
A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :2019 · 12 Apr · Shift 2 · Q39 · MCQ
If a circle of radius R passes through the origin O and intersects the coordinates axes at A and B, then the locus of the foot of perpendicular from O on AB is :2019 · 12 Jan · Shift 2 · Q29 · MCQ
If a circle C, whose radius is 3, touches externally the circle, $x^{2} + y^{2} + 2 x - 4 y - 4 = 0$ at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :2018 · 16 Apr · Shift 1 · Q46 · MCQ
If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles $cos^{- 1} (\frac{1}{7})$ and sec $-$ 1 (7) at the center respectivey, then the distance between…2017 · 8 Apr · Shift 1 · Q41 · MCQ
If a point P has co-ordinates (0, $-$ 2) and Q is any point on the circle, x2 + y2 $-$ 5x $-$ y + 5 = 0, then the maximum value of (PQ)2 is :2017 · 8 Apr · Shift 1 · Q46 · MCQ
The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60o. If the area of the quadrilateral is $43$ , then the perimeter of the quadrilateral is :2017 · 9 Apr · Shift 1 · Q31 · MCQ
A line drawn through the point P(4, 7) cuts the circle x2 + y2 = 9 at the points A and B. Then PA⋅PB is equal to :2017 · 9 Apr · Shift 1 · Q44 · MCQ
A circle passes through (−2, 4) and touches the y-axis at (0, 2). Which one of the following equations can represent a diameter of this circle?2016 · 9 Apr · Shift 1 · Q31 · MCQ
If one of the diameters of the circle, given by the equation, $x^{2} + y^{2} - 4 x + 6 y - 12 = 0,$ is a chord of a circle $S$ , whose centre is at $(- 3, 2)$ , then the radius of $S$ is :2016 · Shift 0 · Q32 · MCQ
Locus of the image of the point $(2, 3)$ in the line $(2 x - 3 y + 4) + k (x - 2 y + 3) = 0, k \in R,$ is a :2015 · Shift 0 · Q37 · MCQ
The length of the diameter of the circle which touches the $x$ -axis at the point $(1, 0)$ and passes through the point $(2, 3)$ is :2012 · Shift 0 · Q38 · MCQ
The circle $x^{2} + y^{2} = 4 x + 8 y + 5$ intersects the line $3 x - 4 y = m$ at two distinct points if :2010 · Shift 0 · Q42 · MCQ
Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $(- 1, 0)$ is equal to $\frac{1}{3}$ . Then the…2009 · Shift 0 · Q39 · MCQ
The point diametrically opposite to the point $P (1, 0)$ on the circle $x^{2} + y^{2} + 2 x + 4 y - 3 = 0$ is :2008 · Shift 0 · Q46 · MCQ
If the lines $3 x - 4 y - 7 = 0$ and $2 x - 3 y - 5 = 0$ are two diameters of a circle of area $49 π$ square units, the equation of the circle is :2006 · Shift 0 · Q78 · MCQ
Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of $\frac{2 π}{3}$ at its center is :2006 · Shift 0 · Q79 · MCQ
If a circle passes through the point (a, b) and cuts the circle $x^{2} + y^{2} = p^{2}$ orthogonally, then the equation of the locus of its centre is :2005 · Shift 0 · Q104 · MCQ
If the circles $x^{2} + y^{2} + 2 a x + cy + a = 0$ and $x^{2} + y^{2} - 3 a x + d y - 1 = 0$ intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for :2005 · Shift 0 · Q105 · MCQ
If the pair of lines $a x^{2} + 2 (a + b) x y + b y^{2} = 0$ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then :2005 · Shift 0 · Q106 · MCQ
If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $10 π$ , then the equation of the circle is :2004 · Shift 0 · Q109 · MCQ
If a circle passes through the point (a, b) and cuts the circle $x^{2} + y^{2} = 4$ orthogonally, then the locus of its centre is :2004 · Shift 0 · Q110 · MCQ
Intercept on the line y = x by the circle $x^{2} + y^{2} - 2 x = 0$ is AB. Equation of the circle on AB as a diameter is :2004 · Shift 0 · Q111 · MCQ
The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is :2003 · Shift 0 · Q113 · MCQ
If the chord y = mx + 1 of the circle $x^{2} + y^{2} = 1$ subtends an angle of measure $4 5^{\circ}$ at the major segment of the circle then value of m is :2002 · Shift 0 · Q114 · MCQ
The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $3 a$ is :2002 · Shift 0 · Q83 · MCQ