The cosine of the acute angle between the curves y = x 2 - 1 and y = x 2 - 3 at their points of intersection is

Step-by-step solution

For points of intersection P   &   Q , solving the curves x 2 - 1 = x 2 - 3 , we get, ⇒ x 2 - 1 = 3 - x 2 ⇒ x = ± 2 ⇒ P 2 , 1   &   Q - 2 , 1 For the slope of tangents at x = 2 C 1 is y = x 2 - 1 d y d x = 2 x ⇒ m 1 = 2 2 And C 2 is y = 3 - x 2 d y d x = − 2 x ⇒ m 2 = - 2 2 ∴ tan ⁡ θ = m 1 - m 2 1 + m 1 m 2 = 4 2 1 - 8 = 4 2 7 ∴ cos ⁡ θ = 7 9