If lines represented by `(1+sin^(2)theta)x^(2)+2hxy+2sinthetay^(2)=0,theta in [0,2pi]` are perpedicular to each other then `theta=`. . . .

Options

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

Answer

C

Explanation

We have, pair of lines represented by
`(1+sin^(2)theta)x^(2)+2hxy+2sinthetay^(2)=0, theta in [0,2pi]`
`therefore(1+sin^(2)theta)+2sintheta=0`
`implies(1+sintheta)^(2)=0 implies1+sintheta=0`
`implies theta=-1=-"sin"(pi)/(2)=sin(2pi-(pi)/(2))`
`implies sintheta="sin"(3pi)/(2)impliestheta=(3pi)/(2)`