If the latusrectum of an ellipse subtends a right angle at the centre of that ellipse, then the eccentricity of that ellipse is

Step-by-step solution

Let equation of ellipse x^2 a^2 + y^2 b^2 =1 Let L L^ is latusrectum, then co-ordinate of L (a e, b^2 a ) L L^ subtend / 2 Angle at the centre, so angle L C S= / 4 array rlrl & 4 & = b^2 a a e & 1 & = b^2 a^2 e & a^2 e & =b^2=a^2 (1-e^2 ) & e & =1-e^2 & e^2+e-1 & =0 & & e & = -1 5 2 e= 5 -1 2 . array