Question

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

Options

• (x - 5) (y - 3) = 0

• x² - y² - 10x + 6y + 16 = 0 

• xy = 0

• xy - 5x - 3y + 15 = 0

Answer 1

The joint equation of bisectors of angles between lines x = 5 and y = 3 is x² - y² - 10x + 6y + 16 = 0.

Explanation:

The equations of bisectors are,

y - 3 = (1)(x - 5) and y - 3 = (-1)(x - 5)

⇒ x - y - 2 = 0 and x + y - 8 = 0

∴ The joint equation of the bisectors is

(x - y - 2)(x + y - 8) = 0

⇒ x² - y² - 10x + 6y + 16 = 0