If tangent at (1, 2) to the circle `C_1: x^2+y^2= 5` intersects the circle `C_2: x^2 + y^2 = 9` at A and B and tangents at A and B to the second circle meet at point C, then the co- ordinates of C are given by

Options

A. `(4,5)`
B. `((9)/(15),(18)/(5))`
C. `(4,-5)`
D. `((9)/(5),(18)/(5))`

Answer

D

Explanation

Tangent at `(1,2)` to the circle `x^(2)+y^(2) =5` is:
`x +2y -5 =0`
Chord of contact from `C(h,k)` to `x^(2) +y^(2) =9` is:
`hx +ky -9 =0`
comparing both equations, we get
`(h)/(1) =(k)/(2) =(9)/(5)`
`rArr (h,k) -= ((9)/(5),(18)/(5))`