If the centroid of the triangle formed by the lines 2 y 2 + 5 x y - 3 x 2 = 0 and x + y = k is 1 18 , 11 18 , then the value of ' k ' equals_____

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Given equations 2 y 2 + 5 x y - 3 x 2 = 0 and x + y = k - - - ( I ) . Given is a homogenous pair of straight lines. 3 x 2 - 5 x y - 2 y 2 = 0 ⇒ 3 x 2 - 6 x y + x y - 2 y 2 = 0 ⇒ 3 x x - 2 y + y x - 2 y = 0 ⇒ x - 2 y 3 x + y = 0 Lines are x - 2 y = 0 - - - ( I I )   &   3 x + y = 0 I I I Intersection of above two lines is origin. Intersection of I   &   I I y = k 3   ,   x   =   2 k 3   ⇒ A 2 k 3 , k 3 Intersection of I   &