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Shift the origin to a suitable point so that the equation $y^{2} + 4 y + 8 x - 2 = 0$ will not contain y and constant terms is

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$(3 / 4, - 2)$

$(3 / 4, 2)$

$(2, 3 / 4)$

$(2, - 3 / 4)$

answer is A.

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Detailed Solution

$y^{2} + 8 x + 4 y - 2 = 0$ New origin $= (h, k)$

${(Y + k)}^{2} + 8 (X + h) + 4 (Y + k) - 2 = 0$

Coeff of $Y = 0 \Rightarrow k^{2} + 8 h + 4 k - 2 = 0$

$\Rightarrow h = \frac{3}{4}$

$∴ New origin = (\frac{3}{4}, - 2)$

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