Question

The straight line $x-2y+1=0$ intersects the circle $x^2+y^2=25$ in points T and T', find the co-ordinates of a point of intersection of tangents drawn at T and T' to the circle.

Answer 1

$x^2+y^2=25$

$x{x}_1+y{y}_1=25$

$\Rightarrow \left(\frac{x_1}{25}\right)x+\left(\frac{y_1}{25}\right)+1=0$

$x-2y+1=0.......L$

Line $L$ is a chord of contact whose eq is:

$x_{1}x+y_{1}y+g(x+x_1)+f(y_1+y)+C=0$

$\therefore \frac{x_1}{25}=1$

$\Rightarrow x_1=25$

$\frac{y_1}{25}=-2$

$\Rightarrow y_1=-50$

$\therefore$ point of intersection $=(25,-50)$