The triangle formed by the lines 2x^2 - 3xy - 2y^2 = 0 and 3x - y = 7 is...

Step-by-step solution

The given equation of the pair of straight lines is 2x^2 - 3xy - 2y^2 = 0 . Factorizing the equation: 2x^2 - 4xy + xy - 2y^2 = 0 2x(x - 2y) + y(x - 2y) = 0 (2x + y)(x - 2y) = 0 The equations of the two lines are L₁: 2x + y = 0 and L₂: x - 2y = 0 . The slopes of these lines are m₁ = -2 and m₂ = 1 2 . Since m₁ m₂ = -2 1 2 = -1 , the lines L₁ and L₂ are perpendicular to each other. Thus, the triangle is right-angled. The equation of the third line is L₃: 3x - y = 7 , which has a slope m₃ = 3 . Let ₁ be the angle betwe