JEE Main 2019MathematicsParabolaMediumMCQ

JEE Main 2019 — Parabola Question with Solution

JEE Main 2019 (12 Apr Shift 2)

Question

The tangents to the curve y=x-22-1 at its points of intersection with the line x-y=3, intersect at the point:

Choose an option

Show full solutionCorrect option: B
Correct answer
B52,-1

Step-by-step explanation

Let coordinates of C be h,k

chord of contact of C w. r. t. y=x-22-1

⇒y=x2-4x+3 is T=0

y+k2=xh+3-2x+h

⇒2h-2x-y=-6-4h-k 

compare it with x-y=3

2h-2=1⇒h=52

6-4h-k=-3 ⇒k=-1

∴ C is 52,-1

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About this question

This is a previous-year question from JEE Main 2019, 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.