The joint equation of bisectors of angles between lines x = 5 a n d y = 3 is _______

Step-by-step solution

We can say that both line passes through point ( 5 , 3 ) and makes angle 45 o a n d 135 o with x-axis ∴ Equation of first line is, y - 3 = tan ⁡ 45 o ( x - 5 ) y - 3 = x - 5 y - x + 2 = 0 .....(i) Similarly, y - 3 = tan ⁡ 135 o ( x - 5 ) y - 3 = - 1 ( x - 5 ) y + x - 8 = 0 ...... (ii) ∴ Joint equation of line is y - x + 2 y + x - 8 = 0 ⇒ x 2 - y 2 - 10 x + 6 y + 16 = 0