Question

The conic represented by the equation $13x^2-18xy+37y^2+2x+14y-2=0$ is

• A. a circle
• B. an ellipse
• C. a parabola
• D. a hyperbola

Answer 1

The correct option is B an ellipse

On comparing the given equation with the equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$
we get,
$a=13,b=37,c=-2,f=7,g=1,\text{and}h=-9$
$△=abc+2fgh-a{f}^2-b{g}^2-c{h}^2$
$=-962-126-637-37+162\ne 0$
and $h^2-ab=81-13\times 37<0$
Thus, we have
$△\ne 0\text{and}{h}^2<ab.$
So, the given equation represents an ellipse.