JEE Main 2020 — Parabola Question with Solution
From: JEE Main 2020 (Online) 8th January Evening Slot
Question
Let a line y = mx (m > 0) intersect the parabola,
y2 = 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 (OPQ) = 4 sq. units, then m is equal
to __________.
Enter your answer
Show full solutionCorrect answer: 0.5
Correct answer
0.5
Step-by-step explanation
let P(t2 , t)
Tangent at P(t2 , t)
ty =
2ty = x + t2
Q = (-t2, 0)
Given (OPQ) = 4
{1 \over 2}\left| {\matrix{ 0 & 0 & 1 \cr {{t^2}} & t & 1 \cr { - {t^2}} & 0 & 1 \cr } } \right| = 4
= 8
t = 2
and P = (4, 2)
As y = mx
2 = 4m
m = 0.5
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