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…
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
$(1,-3)$
$(2,3)$
$(-2,3)$
$(1,3)$
Solution
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 $\left(\frac{h f-b g}{a b-h^2}, \frac{g h-a f}{a b-h^2}\right)$
$\begin{aligned} & =\left(\frac{-22+10}{10-4}, \frac{-4+22}{10-4}\right) \\ & =\left(\frac{-12}{6}, \frac{18}{6}\right)=(-2,3)\end{aligned}$