Question

The conic represented by the equation $2xy+4x-6y+17=0$ is

• A. an ellipse
• B. a pair of straight line
• C. a parabola
• D. a hyperbola

Answer 1

The correct option is D a hyperbola

On compairing the given equation with $a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$, we get
$a=b=0,c=17,g=2,f=-3,h=1$
$\therefore \Delta =abc+2fgh-a{f}^2-b{g}^2-c{h}^2=-29\ne 0$
and $h^2-ab=1-0>0$
Hence $\Delta \ne 0,h^2>ab$
So the given equation represents a hyperbola.