Let `P,Q,R` and `S` be the feet of the perpendiculars drawn from point `(1,1)` upon the lines `y=3x+4,y=-3x+6` and their angle bisectors respectively. Then equation of the circle whose extremities of a diameter are `R` and `S` is

Explanation

,brgt Given lines intersect at point A(`1//3,5)`.
Angle bisectors are always perpendicular.
So, if RS is diameter, then AB is also a diameter.
`:. `Equation of the circle whose diameter is RS
`-=` Equationof circle whose diameter is AB
`-=(x-1)(x-1//3)+(y-5)(y-1)=0 `
`-=3x^(2)+3y^(2)-4x-18y+16=0`