If `r(1-m^2)+m(p-q)=0`, then a bisector of the angle between the lines represented by the equation `px^2-2rxy+qy^2=0`, is.

Options

A. `y=x`
B. `y=-x`
C. ` y=mx`
D. ` ym=x`

Answer

C

Explanation

Given , `px^2-2rxy+qy^2=0`
and `r(-m^2)+m(p-q)=0`
`rArr r(-m^2)=-(p-q)m`
`rArr (1-m^2)/(m)=-((p-q))/(r)` ....(ii)
Equation of bisector of the angle subtended by the line represented by Eq.(i) is
and `(x^2-y^2)/(p-q)=(xy)/(-r)`
`rArr (x^2-y^2)/(xy)=(p-q)/(-r)=(1-m^2)/(m)`
`rArr mx^2+(m^2-1)xy-my^2=0`
`rArr mx^2+m^2xy-xy-my^2=0`
`rArr mx(x+my)-y(x+my)=0`
`rArr (x+my)(mx-y)=0`
`rArr x+my=0 or mx-y=0 rArr x=-my or y=mx` .