JEE Main 2019 — Ellipse Question with Solution
From: JEE Main 2019 (Online) 9th April Evening Slot
Question
If the tangent to the parabola y2 = x at a point
(, ), ( > 0) is also a tangent to the ellipse,
x2 + 2y2 = 1, then is equal to :
Choose an option
Show full solutionCorrect option: A
Correct answer
A
Step-by-step explanation
Point P(, ) is on the parabola y2 = x
...........(1)
Equation of tangent to the parabola y2 = x
at (, ) is T = 0
For this straight line, m = and c =
This tangent is also a tangent to ellipse x2 + 2y2 = 1.
and .
We know the condition of tangency on ellipse is
and
...........(1)
Equation of tangent to the parabola y2 = x
at (, ) is T = 0
For this straight line, m = and c =
This tangent is also a tangent to ellipse x2 + 2y2 = 1.
and .
We know the condition of tangency on ellipse is
and
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This is a previous-year question from JEE Main 2019, covering the Ellipse chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.