JEE Main 2022 · 24 Jun · Shift 2 · Mathematics Q8

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MathematicsSingle correct+4 / -1Question 8 of 90

A particle is moving in the $xy$ -plane along a curve $C$ passing through the point $(3,3)$ . The tangent to the curve $C$ at the point $P$ meets the $x$ -axis at $Q$ . If the $y$ -axis bisects the segment $PQ$ , then $C$ is a parabola with

length of latus rectum 3

length of latus rectum 6

focus

\left(\dfrac43,0\right)

focus

\left(0,\dfrac34\right)

Answer and worked solution

Official answer: A

Tangent meets the $x$ -axis at $Q\left(x-\dfrac y{y'},0\right)$ .

Midpoint on the $y$ -axis. $x+x-\dfrac y{y'}=0$ , so $\dfrac{dy}{dx}=\dfrac y{2x}$ , giving $y^2=cx$ .

Through (3, 3). $c=3$ : $y^2=3x$ , whose latus rectum is 3 (focus $\left(\frac34,0\right)$ ).

(A)

Topics:Formation and applications Parabola Tangents and normals

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JEE Main 2022 · 24 Jun · Shift 2, Mathematics question 8