JEE Main 2024MathematicsCircleMediumNumerical

JEE Main 2024 — Circle Question with Solution

JEE Main 2024 (30 Jan Shift 2)

Question

Consider two circles C1:x2+y2=25 and C2:(x-α)2+y2=16, where α∈(5,9). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of C1and C2 be sin-1638. If the length of common chord of C1 and C2 is β, then the value of (αβ)2 equals _________.

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Show full solutionCorrect answer: 1575
Correct answer
1575

Step-by-step explanation

Given,

C1:x2+y2=25, C2:(x-α)2+y2=16 and 5<α<9

Now, plotting the diagram we get,

Also, given sinθ=638

Now, from the above diagram, finding the area of  ΔOAP we get, 

ΔOAP=12×αβ2=12×5×4sinθ

⇒αβ=40×638

⇒αβ=5×63

⇒(αβ)2=25×63=1575

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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.