The point from which the tangents to the circles `x^2 +y^2-8x + 40 = 0,5x^2+5y^2 -25x +80=0,`and `x^2 +y^2-8x + 16y + 160 = 0` are equal in length, is

Options

A. (8, 15/2)
B. (-8, 15/2)
C. (8, -15/2)
D. none of these

Answer

C

Explanation

The required point is the radical centre of the three given circles.
The radical axes of these three circles taken in pairs are:
`3x-24=0, 16y+120=0 and , -3x+16y+80=0`
Solving any two of these three equations, we get
`x=8, y=-(15)/(2)`
Hence, the required point is (8, -15/2)