$P (5, 5)$ is a point on the circle $x^{2} + y^{2} - 4 x - 6 y - 12 = 0$ . If the origin is translated to a certain point and the transformed equation is $x^{2} + y^{2} = 25$ , then the new point $P =$

(3, 2)

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(1, 2)

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(7, 8)

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(0, 0)

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Solution

The correct option is A $(3, 2)$
Let origin be shifted to (h,k) then
$x = x + h; y = Y + K$
${(x + h)}^{2} + {(y + k)}^{2} - 4 (x + h) - 6 (y + K) - 12 = 0$
$x^{2} + y^{2} + 2 h x - 4 x + 2 k y - 6 y - 4 h - 6 k - 12 + h^{2} + k^{2} = 0$
$\Rightarrow h = 2, k = 3$
$5 = x + 2$ ; $5 = 3 + y$
$\Rightarrow x = 3$ ; $y = 2$

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