JEE Main 2023MathematicsParabolaHardNumerical

JEE Main 2023 — Parabola Question with Solution

JEE Main 2023 (29 Jan Shift 2)

Question

A triangle is formed by the tangents at the point (2,2) on the curves y2=2x and x2+y2=4x, and the line x+y+2=0. If r is the radius of its circumcircle, then r2 is equal to

Enter your answer

Show full solutionCorrect answer: 10
Correct answer
10

Step-by-step explanation

Let

S1:y2=2x

S2:x2+y2=4x

P(2,2) is common point on S1& S2

Let T1 is tangent to S1 at P2,2, then

T1:2y=x+2

⇒T1:x-2y+2=0

And, T2 is tangent to S2 at P2,2, then

T2:2x+2y=2x+2

⇒T2:y=2

And,  L3:x+y+2=0

PQ=a=20

QR=b=8

RP=c=6

Also, ar∆PQR=12221-201-421

⇒ar∆PQR=12221-4-20-600

⇒ar∆PQR=12-60+2=6

∴r=abc4Δ=1604=10

⇒r2=10

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Parabola chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2023, 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.