If tangents are drawn to the circle $x^2+y^2=12$ at the points where it intersects the circle $x^2+y^2-5 x+3 y-2=0$, then the coordinates of the point of intersection of those tangents are

Question

Aicharya · Accepted Answer

Let $(h, k)$ be the point of intersection of the tangents. Then, the chord of contact of tangents is the common chord of the circles $x^2+y^2=12$ and $x^2+y^2-5 x+3 y-2=0$.

The equation of the common chord is

Eqs. (i) and (ii) represents the same line. Therefore, $ \begin{aligned} & \frac{h}{5}=\frac{k}{-3}=\frac{-12}{-10} \\ \Rightarrow \quad & h=6, k=\frac{-18}{5} \end{aligned} $ Hence, the required point is $\left(6,-\frac{18}{5}\right)$

If tangents are drawn to the circle $x^2+y^2=12$ at the points where it intersects the circle $x^2+y^2-5 x+3…

Solution