Question

The curve $5x^2+12xy-22x-12y-19=0$ is.

• A. Ellipse
• B. Parabola
• C. Hyperbola
• D. Parallel straight lines

Answer 1

The correct option is C Hyperbola

The given curve is $5x^2+12xy-22x-12y-19=0$ ....... $\left(i\right)$

Comparing the given curve with general form

$a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$

We get, $a=5,b=0,h=6,g=-11,f=-6,c=-19$

$\Delta =abc+2fgh-a{f}^2-b{g}^2-c{h}^2$

$=\left(5\right)\left(0\right)(-19)+2(-6)(-11)\left(6\right)-5\left(36\right)-0\left(121\right)+19\left(36\right)$

$=0+792-180-0+684=1296\ne 0$

Now, $ab-h^2=5\times 0-36=-36<0$

$\therefore ab-h^2<0$

$\therefore$ The given curve is a hyperbola.