JEE Main 2020MathematicsCircleMediumMCQ

JEE Main 2020 — Circle Question with Solution

JEE Main 2020 (04 Sep Shift 2)

Question

The circle passing through the intersection of the circles, x2+y2-6x=0 and x2+y2-4y=0 having its centre on the line, 2x-3y+12=0, also passes through the point :

Choose an option

Show full solutionCorrect option: B
Correct answer
B(–3,6)

Step-by-step explanation

By family of circle, circle passing through intersection of given circles will be member of

S1+λS2=0 family (λ≠1)

x2+y2-6x+λx2+y2-4y=0

(λ+1)x2+(λ+1)y2-6x-4λy=0

x2+y2-6λ+1x-4λλ+1y=0

 Centre 3λ+1,2λλ+1

Centre lies on 2x-3y+12=0

23λ+1-32λλ+1+12=0

6λ+18=0

λ=-3

Now circle is:x2+y2+3x-6y=0

Now check each option

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About this question

This is a previous-year question from JEE Main 2020, 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.