JEE Main 2022MathematicsCircleEasyNumerical

JEE Main 2022 — Circle Question with Solution

JEE Main 2022 (24 Jun Shift 2)

Question

Let a circle C:x-h2+y-k2=r2,k>0, touch the x-axis at 1,0. If the line x+y=0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h+k+r is equal to _____.

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Show full solutionCorrect answer: 7
Correct answer
7

Step-by-step explanation

Since the circle is touching x-axis so, k=r and h=1

Now by diagram, OP=r,PR=1

OR=r+12

r2=1+r+122

2r2=2+r2+1+2r

r2-2r-3=0

r-3r+1=0

r=3,-1

h+k+r=1+3+3

=7

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About this question

This is a previous-year question from JEE Main 2022, 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.