JEE Main 2022MathematicsCircleMediumMCQ

JEE Main 2022 — Circle Question with Solution

JEE Main 2022 (27 Jun Shift 2)

Question

The set of values of k for which the circle C:4x2+4y2-12x+8y+k=0 lies inside the fourth quadrant and the point 1,-13 lies on or inside the circle C is

Choose an option

Show full solutionCorrect option: D
Correct answer
D9,929

Step-by-step explanation

Given equation of circle C:4x2+4y2-12x+8y+k=0

⇒x2+y2-3x+2y+k4=0

Centre 32,-1;r=13-k2⇒k≤13    …1

case (i) Point 1,-13 lies on or inside circle C

⇒S1≤0⇒k≤929    ⋯2

case (ii) C lies in 4th quadrant

r<1

⇒13-k2<1

⇒k<9    ⋯3

Hence from equation 1∩2∩3⇒k∈(9,929]

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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.