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x^2 +y^2 = 16 and x^2 +y^2=36 are two ci...

`x^2 +y^2 = 16 and x^2 +y^2=36` are two circles. If `P and Q` move respectively on these circles such that `PQ=4` then the locus of mid-point of `PQ` is a circle of radius

A

`sqrt(20)`

B

`sqrt(22)`

C

`sqrt(30)`

D

`sqrt(32)`

Text Solution

Verified by Experts

The correct Answer is:
B
Using Apollonius theorem in `DeltaPCQ`, we get

`CP^(2) + CQ^(2) = 2(CR^(2) +RQ^(2))`
`rArr 16 + 36 =2 (CR^(2) + ((4)/(2))^(2))`
`rArr 52 = 2(CR^(2) +4)`
`rArr CR = sqrt(22)`
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