If S and S^ are the foci of an ellipse, B is one end of the minor axis and S B S^ =90^ , then the eccentricity of that ellipse is

Step-by-step solution

S and S^1 are the foci of an ellipse Coordinate of foci =( a e, 0) Slope of S B= b a e Slope of S^1 B= -b a e Now, S B S^ =90 So, slope of S B slope of S^ B=-1 array ll & b a e (- b a e )=-1 & b^2 a^2 e^2 =1 b^2=a^2 e^2 array We know that, aligned b^2 & =a^2 (1-e^2 ) a^2 e^2 & =a^2 (1-e^2 ) e^2=1-e^2 2 e^2 & =1 e= 1 2 aligned