Let P = (-1, 0), Q = (0, 0) and R = (3, `3sqrt3`) be three points. The equation of the bisector of the angle PQR

Options

A. `y=sqrt3x`
B. `sqrt3y=x`
C. `y=-sqrt3x`
D. `sqrt3y=-x`

Answer

C

Explanation

Given P = (-1,0) O = (0,0) and Q = `(3,3sqrt3)`
Equation of line OP is
`y/x= 0/(-1-0) Rightarrow y=0`

nad equation of line OQ is
`y/x = (3sqrt3 -0)/(3-0)`
` Rightarrow y= sqrt3x`
Angle bisector of lines y = 0 and ` y = sqrt3 x`will be
` y/(sqrt(1^(2) +0^(2)) = +- ((y-sqrt3x))/(sqrt(1+3))`
` Rightarrow y= +- ((y-sqrt3x))/2`
` Rightarrow y = - sqrt3 x or sqrt3 y =x`
Hence, required equation is `y = -sqrt3x `