The equation x^2-3 x y+2 y^2+3 x-5 y+2=0 represents a pair of straight lines. If is the angle between them, then the value of is equal to

Step-by-step solution

The angle between the pair of straight lines represented by x^2-3 x y+2 y^2+3 x-5 y+2=0 is determined using the standard formula for pairs of lines in the general form ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 . Comparing coefficients, we find a = 1 , 2h = -3 h = -3/2 , and b = 2 . The condition = abc + 2fgh - af^2 - bg^2 - ch^2 = 0 confirms the equation represents a pair of lines. The angle between the lines is given by = | 2 h^2-ab a+b | . Substituting values: h^2 = 9/4 , ab = 2 , so h^2 - ab = 1/4 and a+b = 3 , yie