JEE Main 2024MathematicsCircleEasyMCQ

JEE Main 2024 — Circle Question with Solution

JEE Main 2024 (30 Jan Shift 1)

Question

If the circles (x+1)2+(y+2)2=r2 and x2+y2-4x-4y+4=0 intersect at exactly two distinct points, then

Choose an option

Show full solutionCorrect option: C
Correct answer
C3<r<7

Step-by-step explanation

Given,

S1≡x+12+y+22=r2 and S2≡x2+y2-4x-4y+4=0 or S2≡x-22+y-22=22

Now, if two circles intersect at two distinct points then r1-r2<C1C2<r1+r2.

⇒r-2<32+42<r+2

⇒r-2<5<r+2

⇒r-2<5 and r+2>5

⇒-5<r-2<5 and r>3

⇒-3<r<7 and r>3

⇒3<r<7

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About this question

This is a previous-year question from JEE Main 2024, 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.