JEE Main 2021 — Parabola Question with Solution
From: JEE Main 2021 (Online) 25th February Evening Shift
Question
The shortest distance between the line x y = 1 and the curve x2 = 2y is :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
Shortest distance must be along common normal
Let a point on curve has x coordinate = h
Then y coordinate :
h2 = 2y
y =
So point is = (h, )
m1 (slope of line x y = 1) = 1
slope of perpendicular line = 1
Slope of the perpendicular line on the curve x2 = 2y,
Slope of normal =
= 1 h = 1
So point is
Let a point on curve has x coordinate = h
Then y coordinate :
h2 = 2y
y =
So point is = (h, )
m1 (slope of line x y = 1) = 1
slope of perpendicular line = 1
Slope of the perpendicular line on the curve x2 = 2y,
Slope of normal =
= 1 h = 1
So point is
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This is a previous-year question from JEE Main 2021, covering the Parabola 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.