The curve `5x^(2)+12xy-22x-19=0`is

Options

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

Answer

C

Explanation

The given curve is `5x^(2)+12xy-22x-22x-12y-19=0` comparing the curve (i) with general from `ax^(2) +by^(2)+2hxy+2gx+2fy+c=0,we get a=5,h=6,b=0,g=-11,f=-6,c=-19 alpha =abc+2fgh-af^(2)-bg^(2)-ch^(2)`=5x0x(-19)+2x(-6)(-11)(6)-x36-0-(-19)(36) `Delta=792-180+19x36ne0`
`thereforeDeltane0`
`rArrab -h^2=0-36=-36`
therefore ab-h^(2) lt 0` so, the curve is a hyperbola.