The angle of intersection between the curves y^2+x^2=a^2 2 and x^2-y^2=a^2 is

Step-by-step solution

Given curves, y^2+x^2=a^2 2 and x^2-y^2=a^2 On solving eqs. (i) and (ii), we get the point of intersection x=a 2 +1 2 , y=a 2 -1 2 Now, for curve -1: y^2+x^2=a^2 2 aligned & 2 y ( d y d x )₁+2 x=0 ( d y d x )₁=- x y =m₁ & m₁= -a 2 +1 2 a 2 -1 2 =- 2 +1 2 -1 aligned and curve -2: x^2-y^2=a^2 On differentiating aligned & ( d y d x )₂= x y & m₂=- 2 +1 2 -1 aligned Then, = m₁-m₂ 1+m₁ m₂ aligned & = - 2 +1 2 -1 - 2 +1 2 -1 1+ (- 2 +1 2 -1 ) ( . 2 +1 2 -1 ) . & = -2 2 +1 2 -1 1- 2 +1 2 -1 & = -2 ( 2 +1)( 2 -1) 2 -1- 2 -1