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 condition is
`x^(2) (cos^(2) theta-1) -xy sin^(2) theta + y^(2)`
`sin^(2)theta = 0`
Here, `a = cos^(2)theta -1, h = -(1)/(2) sin^(2)theta`,
`b = sin^(2)theta`
`a + b = cos^(2) theta + sin^(2) theta -1 = 1 - 1 =0`
`therefore` The angle between the pair of straight lines is `(pi)/(2)`