If the straight line `x - 2y + 1 = 0` intersects the circle `x^2 + y^2 = 25` at points P and Q, then find the coordinates of the point of intersection of the tangents drawn at P and Q to the circle `x^2 + y^2 = 25`.

Options

A. (25, -50)
B. (-25, 50)
C. (-25, -50)
D. (25, 50)

Answer

B

Explanation

Let the required point be `R(x_(1), y_(1))`. Then, PQ is the chord of contact of tangents drawn from `R(x_(1), y_(1))` to `x^(2)+y^(2)=25`. So, the equation of `PQ` is `x x_(1)+y y_(1)=25`.
This equations and x-2y+1=0 represent the same line.
`:. (x_(1))/(1)=(y_(1))/(-2)=(-25)/(1)rArr x_(1)=-25` and y = 50.
Hence, the required point is (-25, 50).