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The joint equation of bisectors of angle...

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

A

`(x-5)(y-3)=0`

B

`x^2-y^2-10x+6y+16=0`

C

`xy=0`

D

`xy-5x-3y+15=0`

Text Solution

Verified by Experts

The correct Answer is:
B
The equation of the bisector of tha angle between the lines `(x-5) and (y-3)` is `((x-5))/(sqrt(1^2))=+-(y-3)/(sqrt(1^2))`
`rArr (x-5)/(1)=+-(y-3)/(1)`
`rArr x-5=+(y-3) and x-5=-(y-3)`
`rArr (x-y-2)=0 and (x+y-8)=0`
`therefore` Combind equation of bisector of angle between the lines is `1(x-y-2)(x+y-8)=0`
`rArr x^2+xy-8x-xy-y^2+8y-2x-2y-16=0`
`rArr x^2-y^2-10x-6y+16=0`
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