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

Options

A. ellispe
B. parabola
C. hyperbola
D. parallel striaight lines

Answer

C

Explanation

The given curve is
` 5x^(2) +12xy -22y x -12y -19=0`
Comparing the curve (i) with general form
` ax^(2) +by^(2) +2hxy+ 2gx +2fy + c=0`
we get
` a= 5, h =6 , b=0, g =- 11 `
f= -6, c= -19
` Delta = abc + 2fgh -af^(2) -bg^(2) -ch^(2)`
= `5xx 0 xx (-19) + 2xx (-6) (-11) (6)`
` - 5 xx 36 -0-(-19) (36)`
`Delta= 792 -180 + 19 xx 36 ne 0`
` Delta ne 0`
Now ` ab = 5 xx0 = 0 , h^(2) =36`
`Rightarrow ab - h^(2) =0-36 = -36`
` ab -h^(2) lt 0`
SO the curve is a hyperbola.