Question

What conics do the following equations represent? When possible, find their centres, and also their equations referred to the centre.
$3x^2-8xy-3y^2+10x-14y+8=0.$

Answer 1

$h^2-ac=4^2-8\times 3=-8<0$ and $h\ne 0$

As $h^2-ac<0$,the given equation represents an ellipse

For centre,

$\frac{\delta S}{\delta x}=\frac{\delta S}{\delta y}=0$

$6x-8y+10=06y+8x+14=0$

centre of the ellipse is : $-\frac{43}{25},-\frac{1}{25}$