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The geometric mean of the minimum and ...

The geometric mean of the minimum and maximum values of the distance of point (-7, 2) from the points on the circle `x^(2)+y^(2)-10x-14y-51=0` is equal to

A

`2sqrt(11)`

B

13

C

`5sqrt(5)`

D

12

Text Solution

Verified by Experts

The correct Answer is:
A
Let C be the centre of the given circle and r be its radius. The coordinates of C are (5, 7) and `r=5sqrt(5)`.
The maximum and minimum values of the distances of point P(-7, 2) from the points on the given circle are (CP + r) and (CP-r) respectively.
We have, `CP=sqrt((5+7)^(2)+(7-2)^(2))=13`
Hence, required geometric mean
`=sqrt((13+5sqrt(5))(13-5sqrt(5)))=sqrt(169-125)=2sqrt(11)`
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