The joint equation of bisectors of angles between lines `x=5` and `y=3` is

Options

A. `(x-5)(y-3)=0`
B. `x^2-y^(2)-10x+6y+16=0`
C. `x^2-y^(2)-10x+6y+16=0`
D. `xy=0`

Answer

B

Explanation

The equation of the bisector of the angle between the lines `(x-5) and (y-3)` is
`(((x-5))/(sqrtt^(2)))= pm ((y-3)/(sqrtt^(2))) Rightarrow (x-5)/(1)= pm (y-3)/(1)`
`Rightarrow x-5=+ (y-3) and x-5=-(y-3)`
`Rightarrow (x-y-2)=0 and (x+y-8)=0`
`therefore ` Combined equation of bisector of angle between the lines is
`(x-y-2)(x+y-8)=0`
`Rightarrow x^(2)+xy-8x-xy-y^(2)+8y-2x-2y-16=0`
`Rightarrow x^(2)-y^(2)-10x+6y+16=0`