If the angle between the lines joining the end points of minor axis of the ellipse x^2 a^2 + y^2 b^2 =1 with one of its foci is 2 , then what is the eccentricity of the ellipse?

Step-by-step solution

Given, x^2 a^2 + y^2 b^2 =1 given: P F₁ Q=90^ array ll & m_ P F₁ m_ Q F₁ =-1 & -b a e b a e =-1 & b^2=a^2 e^2 (i) & b^2=a^2 (1-e^2 )...(ii) array From (i) and (ii) we get, aligned & e^2=1-e^2 & 2 e^2=1 & e^2= 1 2 & e= 1 2 aligned