If the equation kx^2 - 5xy + 6y^2 + x - 3y = 0 represents a pair of straight lines, then the co-ordinates of their point of intersection are

Step-by-step solution

Comparing the given equation with the general equation of second degree ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 , we get: a = k , h = - 5 2 , b = 6 , g = 1 2 , f = - 3 2 , c = 0 For the equation to represent a pair of straight lines, the condition is = abc + 2fgh - af^2 - bg^2 - ch^2 = 0 . Substituting the values: 0 + 2 (- 3 2 ) ( 1 2 ) (- 5 2 ) - k (- 3 2 )^2 - 6 ( 1 2 )^2 - 0 = 0 15 4 - 9k 4 - 6 4 = 0 9 4 - 9k 4 = 0 k = 1 The equation of the pair of straight lines is x^2 - 5xy + 6y^2 + x - 3y = 0 . Factorizing the