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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
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Verified Answer
The correct answer is:
$\left(6, \frac{-18}{5}\right)$
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 $\left(6,-\frac{18}{5}\right)$.
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 $\left(6,-\frac{18}{5}\right)$.
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