JEE Main 2019 — Ellipse Question with Solution
From: JEE Main 2019 (Online) 12th April Morning Slot
Question
If the normal to the ellipse 3x2
+ 4y2
= 12 at a point P on it is parallel to the line, 2x + y = 4 and the tangent
to the ellipse at P passes through Q(4,4) then PQ is equal to :
Choose an option
Show full solutionCorrect option: D
Correct answer
D
Step-by-step explanation
Equation of ellipse is
Normal at P(2 cos , ) is 2x sin - = sin cos as the normal is parallel to 2x + y = 4
tangent at P(2 cos , ) is
x cos + 2y sin = 2
Passes through (4, 4)
4 cos + 8 sin = 2 ....... (ii)
From (i) and (ii)
Normal at P(2 cos , ) is 2x sin - = sin cos as the normal is parallel to 2x + y = 4
tangent at P(2 cos , ) is
x cos + 2y sin = 2
Passes through (4, 4)
4 cos + 8 sin = 2 ....... (ii)
From (i) and (ii)
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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.