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Q.
In order to eliminate the first degree terms from the equation $4\,x^2 + 8\,xy + 10\, y^2 - 8\,x - 44\,y + 14 = 0 $ the point to which the origin has to be shifted is
TS EAMCET 2017
Solution:
On comparing the given equation with
$a \,x^{2}+2 h\, x y+b y^{2}+2 \,g x+2\,f y+c=0$, we get
$a=4, h=4, b=10, g=-4, f=-22$ and $c=14$
For removal of first degree terms, shift the origin to
$\left(\frac{b g-f h}{h^{2}-a b}, \frac{a f-g h}{h^{2}-a b}\right) =\left(\frac{-40+88}{16-40}, \frac{-88+16}{16-40}\right)$
$=\left(\frac{48}{-24}, \frac{-72}{-24}\right)=(-2,3) $