If `x^2-2p x y-y^2=0` and `x^2-2q x y-y^2=0` bisect angles between each other, then find the condition.

Options

A. p+q=1
B. pq=1
C. pq+1=0
D. `p^(2)+pq+q^(2)=0`

Answer

C

Explanation

The equation of the bisectors of the angles between the lines `x^(2)-2pxy-y^(2)=0`
`(x^(2)-y^2)/(1-(-1))=(xy)/(-p)`
`(x^(2)-y^2)/(2)=(-xy)/(p)`
`Rightarrow px^(2)+2xy-py^(2)=0`
`(p)/(1)=(2)/(-2q)=-(p)/(-1)`
`Rightarrow pq+1=0`