MHTCET 2016 Math Solved Paper

(b) The equation of the bisectors of the angle between the lines (x =5) and (y = 3) is

(x−5)

√12

=±

y−3

√12

⇒

x−5

1

=±

y−3

1

⇒ x - 5 = + (y - 3 ) and x - 5 = - (y - 3 )
⇒ (x - y - 2 ) = 0 and (x + y - 8) = 0
Hence, combinedequation of bisectors of angle between given lines is (x - y - 2 ) (x +y - 8) = 0
⇒ x2 + xy - 8x - xy - y2 + 8y - 2 x - 2 y - 16 = 0
⇒ x2−y2 - 10x + 6y + 16 = 0