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The ratio of the largest and shortest distances from the point (2, -7) to the circle $x^{2} + y^{2} - 14 x - 10 y - 151 = 0$ is

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3 : 2

14 : 1

15 : 13

7 : 1

answer is D.

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Detailed Solution

$\begin{aligned} c = (7, 5), r = \sqrt{49 + 25 + 151} = 15, P = (2, - 7) \\ c p = \sqrt{25 + 144} = \sqrt{169} = 13 \\ c p + r : | c p - r | = 28 : 2 = 14 : 1 \end{aligned}$

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