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In order to eliminate the first degree terms from the equation $2 x^2+4 x y+5 y^2-4 x-22 y+7=0$, the point to which origin is to be shifted, is
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The correct answer is:
$(-2,3)$
Given equation is
$2 x^2+4 x y+5 y^2-4 x-22 y+7=0$
Here, $a=2, b=5, c=7, h=2, g=-2, f=-11$
To eliminate 1st degree terms origin is to be shifted to the point $\left(\frac{h f-b g}{a b-h^2}, \frac{g h-a f}{a b-h^2}\right)$
$\begin{aligned} & =\left(\frac{-22+10}{10-4}, \frac{-4+22}{10-4}\right) \\ & =\left(\frac{-12}{6}, \frac{18}{6}\right)=(-2,3)\end{aligned}$
$2 x^2+4 x y+5 y^2-4 x-22 y+7=0$
Here, $a=2, b=5, c=7, h=2, g=-2, f=-11$
To eliminate 1st degree terms origin is to be shifted to the point $\left(\frac{h f-b g}{a b-h^2}, \frac{g h-a f}{a b-h^2}\right)$
$\begin{aligned} & =\left(\frac{-22+10}{10-4}, \frac{-4+22}{10-4}\right) \\ & =\left(\frac{-12}{6}, \frac{18}{6}\right)=(-2,3)\end{aligned}$
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