Find the greatest distance of the point `P(10 ,7)` from the circle `x^2+y^2-4x-2y-20=0`

Options

A. 10
B. 15
C. 5
D. none of these

Answer

B

Explanation

We have,
`S_(1)=10^(2)+7^(2)-4xx10-2xx7-20 gt 0`.
So, P lies outside the circle.
Join P with the centre C(2, 1) of the given circle. Suppose PC cuts the circle at A and B. Then, PB is the greatest distance of P from the circle.
Now, we have
`PC=sqrt((10-2)^(2)+(7-1)^(2))=10`
and, CB = Radius = `sqrt(4+1+20)=5`
`:. PB=PC+CB=(10+5)=15`.