The ratio of the largest and shortest distanc | vedclass

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(D) The given equation of the circle is $x^2 + y^2 - 14x - 10y - 151 = 0$. Completing the square,we get $(x - 7)^2 + (y - 5)^2 = 151 + 49 + 25 = 225$.

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$14:1$

Vedclass · Answer

(D) The given equation of the circle is $x^2 + y^2 - 14x - 10y - 151 = 0$. Completing the square,we get $(x - 7)^2 + (y - 5)^2 = 151 + 49 + 25 = 225$. Thus,the center $C = (7, 5)$ and the radius $r = 15$. Let $P = (2, -7)$. The distance $d$ from $P$ to the center $C$ is $d = \sqrt{(7 - 2)^2 + (5 - (-7))^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = 13$. Since $d The shortest distance from $P$ to the circle is $r - d = 15 - 13 = 2$. The largest distance from $P$ to the circle is $r + d = 15 + 13 = 28$. The ratio of the largest to the shortest distance is $28 : 2 = 14 : 1$.

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

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