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  4. A straight line with slope 2 and y-intercept 5 touches the circle x2+y2+16 x+12 y+c=0 at a point Q. Then the coordinates of Q are

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Q. A straight line with slope $2$ and $y$-intercept $5$ touches the circle $x^{2}+y^{2}+16 x+12 y+c=0$ at a point $Q$. Then the coordinates of $Q$ are

Conic Sections

Solution:

image
From the figure, we have
$y_{1}=2 x_{1}+5 $
and $ \frac{y_{1}+6}{x_{1}+8} \times 2=-1$
or $x_{1}=-6$ and $y_{1}=-7$