The centre of the circle passing through the points of intersection of the curves 2 x + 3 y + 4 3 x + 2 y - 1 = 0 and x y = 0 is

Step-by-step solution

Family of curves passing through points of intersection of curves 2 x + 3 y + 4 3 x + 2 y - 1 = 0 and x y = 0 is 2 x + 3 y + 4 3 x + 2 y - 1 + λ x y = 0 ⇒ 2 x 2 + y 2 + 13 x y + 10 x + 5 y - 4 + λ x y = 0 .... ( 1 ) If equation 1 represents a circle then coefficient of x y is zero ⇒ λ = - 13 ⇒ equation of circle is x 2 + y 2 + 5 3 x + 5 6 y - 2 3 = 0 ⇒ center of the circle is - 5 6 , - 5 12