Answer:
Option B
Explanation:
The equation of the bisector of the angle between the lines
(x-5) and (y-3) is
$\frac{(x-5)}{\sqrt{1^{2}}}=\pm\frac{y-3}{\sqrt{1^{2}}}\Rightarrow\frac{x-5}{1}=\pm\frac{y-3}{1}$
$\Rightarrow$ 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
$\Rightarrow x^{2}+xy-8x-xy-y^{2}+8y-2x-2y-16=0$
$\Rightarrow x^{2}-y^{2}-10x+6y+16=0$
