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The normal to the circle given $x^{2} + y^{2} - 6 x + 8 y - 144 = 0 at (8, 8)$ meets the circle again at the point

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(2,- 16

(2,16)

$(- 2, 16)$

$(- 2, - 16)$

answer is D.

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Detailed Solution

Centre of the circle = C (3, - 4). Given point,4 = (8, 8)

Let B be at point at with the normal meets the circle again.

Then midpoint $A B = C \Rightarrow B = 2 C - A = 2 (3, - 4) - (8, 8) = (- 2, - 16)$ .

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