JEE Main 2020MathematicsCircleMediumNumerical

JEE Main 2020 — Circle Question with Solution

JEE Main 2020 (02 Sep Shift 1)

Question

The numbers of integral values of k for which the line, 3x+4y=k intersects the circle, x2+y2-2x-4y+4=0 at two distinct points is....

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Show full solutionCorrect answer: 9
Correct answer
9

Step-by-step explanation

If distance from center to line is less than radius then line cut circle at two distinct point.

Center of circle (1,2), r=1

3+8-k5<1

11-k<5

-5<11-k<5⇒  k∈(6,16)

k=7,8,9,10,11,12,13,14,15

Number of values of k=9.

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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.