The angle between the pair of straight lines `y^(2)sin^(2)theta-xy sin^(2)theta+x^(2)(cos^(2)theta-1)=0` is

Options

A. `(pi)/(3)`
B. `(pi)/(4)`
C. `(pi)/(6)`
D. `(pi)/(2)`

Answer

D

Explanation

The given equation is
`x^(2)(cos^(2)theta-1)-xysin^(2)theta+y^(2)sin^(2)theta=0`
On comparing with
`ax^(2)+2hxy+by^(2)=0`
We get
`a=cos^(2)theta-1`,
`h=-(1)/(2)sin^(2)theta,b=sin^(2)theta`
Now, `a+b=cos^(2)theta+sin^(2)theta-1`
`=1-1=0`
`:.` The angle between the pair of straight lines is `(pi)/(2)`.