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If the equation $y^{2} - 4 x + 6 y + 17 = 0$ changed as $y^{2} = 4 a x$ then shifted origin is

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$(2, 3)$

$(-$ 2,3 $)$

$($ 2, $-$ 3 $)$

$(-$ 2, $-$ 3 $)$

answer is D.

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Detailed Solution

$y^{2} - 4 x + 6 y + 17 = 0$

$y^{2} + 6 y = 4 x - 17$

$y^{2} + 6 y + 9 = 4 x - 17 + 9$

$(y + 3)^{2} = 4 x - 8$

$(y - (- 3))^{2} = 4 (x - 2)$

$(y - k)^{2} = 4 a (x - h)$

$(h, k) = (2, - 3)$

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