Let y = x + 2 , 4 y = 3 x + 6 and 3 y = 4 x + 1 be three tangent lines to the circle ( x - h ) 2 + ( y - k ) 2 = r 2 . Then h + k is equal to :

Step-by-step solution

Lines y = x + 2 , 4 y = 3 x + 6 and 3 y = 4 x + 1 are tangents to the circle ( x - h ) 2 + ( y - k ) 2 = r 2 . Centre of the circle is h , k . Equation of bisector of lines 4 y = 3 x + 6 ,   3 y = 4 x + 1 is: 4 x - 3 y + 1 5 = ± 3 x - 4 y + 6 5 ⇒ 4 x - 3 y + 1 = ± 3 x - 4 y + 6 Taking positive sign, we get 4 x - 3 y + 1 = 3 x - 4 y + 6 ⇒ x + y = 5 Since, centre h , k lies on the bisector, therefore h + k = 5