JEE Main 2021MathematicsCircleHardMCQ

JEE Main 2021 — Circle Question with Solution

JEE Main 2021 (26 Aug Shift 2)

Question

A circle C touches the line x=2y at the point 2,1 and intersects the circle C1:x2+y2+2y-5=0 at two points P and Q such that PQ is a diameter of C1. Then the diameter of C is :

Choose an option

Show full solutionCorrect option: D
Correct answer
D75

Step-by-step explanation

Family of circle touching line 2y=x at point 2,1
(x-2)2+(y-1)2+λ(x-2y)=0   ...(1)
common chord PQ is
(x-2)2+(y-1)2+λ(x-2y)-x2-y2-2y+5=0
(diameter of C1 passes through (0,-1))
4+4+2λ-1+2+5=0

λ=-7 put in equation 1

(x-2)2+(y-1)2-7(x-2y)=0

x2+y2-11x+12y+5=0

r=1214+36-5=121+1244=2454=2452⇒ diameter =245=75

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About this question

This is a previous-year question from JEE Main 2021, covering the Circle 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.