JEE PYQ: Parabola Question 13
Question 13 - 2020 (08 Jan Shift 2)
Let a line $y = mx$ $(m > 0)$ intersect the parabola, $y^2 = x$ at a point $P$, other than the origin. Let the tangent to it at $P$ meet the $x$-axis at the point $Q$. If area $(\Delta OPQ) = 4$ sq. units, then $m$ is equal to ______.
Show Answer
Answer: 0.5
Solution
$P = (t^2, t)$ on $y^2 = x$. Tangent at $P$: $ty = \frac{x+t^2}{2} \Rightarrow Q(-t^2, 0)$. Area $= \frac{1}{2}|t^3| = 4 \Rightarrow t = 2$. $P = (4, 2)$, so $m = \frac{2}{4} = \frac{1}{2}$.
BETA
