JEE Main 2019MathematicsCircleMediumMCQ

JEE Main 2019 — Circle Question with Solution

JEE Main 2019 (08 Apr Shift 1)

Question

The sum of the squares of the lengths of the chords intercepted on the circle,  x2+y2=16, by the lines, x+y=n,  n∈N, where N is the set of all natural numbers is:

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Show full solutionCorrect option: A
Correct answer
A 210

Step-by-step explanation

The length of the perpendicular from centre 0,0  to the line x+y=n is 0+0-n12+I2=n2

Length of intercept =242-n22=64-2n2

⇒ Possible values of n are 1,2,….5

⇒ Sum of the square of lengths of intercepts

=Σn=1564-2n2=64×5-2Σn=15n2

=320-2Σn=15n2=320-110=210

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About this question

This is a previous-year question from JEE Main 2019, 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.