If ⁻¹(a) is the acute angle between the curves x^2+y^2=4 x and x^2+y^2=8 at the point (2,2) , then a is equal to

Step-by-step solution

Given, curves are : x^2+y^2=4 x ...(i) and x^2+y^2=8 ...(ii) d y d x is the slope of tangent drawn to curve Slope of the tangent drawn to curve (i) is m₁= d y d x [from curve (i)] On differentiating Eq. (i) w.r.t. x d d x (x^2+y^2 )= d d x (4 x) 2 x+2 y d y d x =4 d y d x = 4-2 x 2 y . m₁ |_ a t(2,2) = 4-2 2 2 2 =0 On differentiating Eq. (ii) w.r.t. x , d d x (x^2+y^2 )= d d x (8) array ll & 2 x+2 y d y d x =0 & d y d x = -2 x 2 y = -x y array .m₂ |_ (2,2) = -2 2 =-1 = | m₂-m₁ 1+m₁ m₂ |= | -1-0 1+0 |=1 = ⁻¹( l )= 4