JEE Main 2014MathematicsCircleHardMCQ

JEE Main 2014 — Circle Question with Solution

JEE Main 2014 (06 Apr)

Question

Let C  be the circle with center at 1,1 and radius =1. If T is the circle centered at 0,y, passing through the origin and touching the circle C externally, then the radius of T is equal to 

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Show full solutionCorrect option: B
Correct answer
B 1 4

Step-by-step explanation

Let r be the required radius
As origin lies on the circle, the distance of 0,0 from 0,y=r 

∴ y=r



As the two circles touch externally, distance between centres is sum of the radii

⇒0-12+y-12=r+1

⇒1+y2-2y+1=r2+2r+1

⇒1+r2-2r=r2+2r, ∵   y=r

∴1=4r

∴    r=14

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About this question

This is a previous-year question from JEE Main 2014, 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.