The co-ordinate of the point on the circle $x^{2} + y^{2} - 12 x - 4 y + 30 = 0$ , which is farthest from the origin are:

(9, 3)

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(8, 5)

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(12, 4)

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none

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Solution

The correct option is A (9, 3)
C = (6, 2) P = (0, 0) $C P = \sqrt{40} = 2 \sqrt{10}$ $r = \sqrt{10}$
Farthest point B divides $¯ ¯¯¯¯¯¯ ¯ C P$ is in the ratio r : CP + r enternally
r : CP + r = 1 : 3
$B = \frac{3 (6, 2) - 1 (0, 0)}{2} = (9, 3)$

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