New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Straight Lines and Pair of Straight Lines question

2022 · 24 Jun · Shift 1 · Q37

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

PYQ Library
JEE Main
Mathematics
Straight Lines and Pair of Straight Lines
2022 · 24 Jun · Shift 1 · Q37

Straight Lines and Pair of Straight Lines question

2022 · 24 Jun · Shift 1 · Q37

JEE MainMathematicsStraight Lines and Pair of Straight LinesNumerical+4 / −1

Let

A\left( {{3 \over {\sqrt a }},\sqrt a } \right),\,a \gt 0

, be a fixed point in the xy-plane. The image of A in y-axis be B and the image of B in x-axis be C. If

D(3\cos \theta ,a\sin \theta )

is a point in the fourth quadrant such that the maximum area of

\Delta

ACD is 12 square units, then a is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Straight Lines and Pair of Straight Lines

Let the area of the triangle with vertices A(1, $α$ ), B( $α$ , 0) and C(0, $α$ ) be 4 sq. units. If the points ( $- α$ , $- α$ ), ( $α$ , $α$ ) and ( $α$ 2, $β$ ) are collinear, then $β$ is equal to :2022 · MCQ
A line, with the slope greater than one, passes through the point $A (4, 3)$ and intersects the line $x - y - 2 = 0$ at the point B. If the length of the line segment $A B$ is $\frac{29}{3}$ , then $B$ also lies on the line :2022 · MCQ
Let the point $P (α, β)$ be at a unit distance from each of the two lines $L_{1} : 3 x - 4 y + 12 = 0$ , and $L_{2} : 8 x + 6 y + 11 = 0$ . If $P$ lies below $L_{1}$ and above $L_{2}$ , then $100 (α + β)$ is equal to :2022 · MCQ
A point $P$ moves so that the sum of squares of its distances from the points $(- 2, 1)$ and $(- 2, 1)$ is 14. Let $f (x, y) = 0$ be the locus of $P$ , which intersects the $x$ -axis at the points $A$ , $B$ and the $y$ -axis…2022 · MCQ
The equations of the sides $AB, BC$ and $2 x + y = 0, x + p y = 15 a$ of a triangle $ABC$ are $2 x + y = 0, x + p y = 15 a$ and $x - y = 3$ respectively. If its orthocentre is $(2, a), - \frac{1}{2} < a < 2$ , then…2022 · Numerical
Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of $Δ$ PQR is :2022 · MCQ
Let $A (1, 1), B (- 4, 3), C (- 2, - 5)$ be vertices of a triangle $B C$ be a point on side $B C$ , and $Δ_{1}$ and $Δ_{2}$ be the areas of triangles $A P B$ and $A B C$ , respectively. If $Δ_{1} : Δ_{2} = 4 : 7$ , then the area…2022 · MCQ
The equations of the sides $AB, BC$ and CA of a triangle ABC are $2 x + y = 0, x + p y = 39$ and $x - y = 3$ respectively and $P (2, 3)$ is its circumcentre. Then which of the following is NOT true?2022 · MCQ