The measure of the acute angle between the pair of lines 2x^2 + xy - y^2 - x + 2y - 1 = 0 is:

Step-by-step solution

Comparing the given equation 2x^2 + xy - y^2 - x + 2y - 1 = 0 with the general equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 , we get: a = 2 , h = 1 2 , b = -1 The acute angle between the pair of lines is given by: = | 2 h^2 - ab a + b | Substituting the values: = | 2 ( 1 2 )^2 - (2)(-1) 2 + (-1) | = | 2 1 4 + 2 1 | = 2 9 4 = 3 Since = 3 , we can find using the relation = 1 1 + ^2 : = 1 1 + 3^2 = 1 10 = ⁻¹ ( 1 10 ) Answer: ⁻¹ 1 10