New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Parabola question

2025 · 23 Jan · Shift 2 · Q44

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Parabola
2025 · 23 Jan · Shift 2 · Q44

Parabola question

2025 · 23 Jan · Shift 2 · Q44

JEE MainMathematicsParabolaMCQ+4 / −1

Let the shortest distance from

(a, 0), a\gt 0

, to the parabola

y^2=4 x

be 4 . Then the equation of the circle passing through the point

(a, 0)

and the focus of the parabola, and having its centre on the axis of the parabola is :

A
$x^2+y^2-8 x+7=0$
B
$x^2+y^2-6 x+5=0$
C
$x^2+y^2-4 x+3=0$
D
$x^2+y^2-10 x+9=0$

More from Parabola

The focus of the parabola $y^{2} = 4 x + 16$ is the centre of the circle $C$ of radius 5 . If the values of $λ$ , for which C passes through the point of intersection of the lines $3 x - y = 0$ and $x + λ y = 4$ , are $λ_{1}$ and $λ_{2}, λ_{1} < λ_{2}$ …2025 · Numerical
If the equation of the parabola with vertex $V (\frac{3}{2}, 3)$ and the directrix $x + 2 y = 0$ is $α x^{2} + β y^{2} - γ x y - 30 x - 60 y + 225 = 0$ , then $α + β + γ$ is equal to :2025 · MCQ
Let ABCD be a trapezium whose vertices lie on the parabola $y^{2} = 4 x$ . Let the sides AD and BC of the trapezium be parallel to $y$ -axis. If the diagonal AC is of length $\frac{25}{4}$ and it passes through the point…2025 · MCQ
Let $A$ and $B$ be the two points of intersection of the line $y + 5 = 0$ and the mirror image of the parabola $y^{2} = 4 x$ with respect to the line $x + y + 4 = 0$ . If $d$ denotes the distance between $A$ and $B$ , and a denotes the area of $△ S A B$ …2025 · Numerical
Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at the points A and B, then (AB)2 is equal to :2025 · MCQ
Let $y^{2} = 12 x$ be the parabola and $(S P) (S Q) = \frac{147}{4}$ be its focus. Let $P Q$ be a focal chord of the parabola such that $(S P) (S Q) = \frac{147}{4}$ . Let $C$ be the circle described taking $64 x^{2} + 64 y^{2} - α x - 643 y = β$ as a diameter. If the equation of a circle $C$ is $64 x^{2} + 64 y^{2} - α x - 643 y = β$ …2025 · Numerical
Let the line $L : 2 x + y = α$ pass through the point of the intersection $P$ (in the first quadrant) of the circle $x^{2} + y^{2} = 3$ and the parabola $x^{2} = 2 y$ . Let the line $L$ touch two circles $C_{1}$ …2024 · Numerical
Let the length of the focal chord PQ of the parabola $y^{2} = 12 x$ be 15 units. If the distance of $PQ$ from the origin is $p$ , then $10 p^{2}$ is equal to .2024 · Numerical