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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 co-ordinates of Q are

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$(- 6, 11)$

$(- 9, - 13)$

$(- 10, - 15)$

$(- 6, - 7)$

answer is D.

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Detailed Solution

Let $Q = (x_{1}, y_{1})$ . Then

we have $y_{1} = 2 x_{1} + 5$ and $\frac{y_{1} + 6}{x_{1} + 8} \times 2 = - 1$

$\Rightarrow x_{1} = - 6$ and $y_{1} = - 7$

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