If O B is the semi-minor axis of an ellipse, F 1 and F 2 are its focii and the angle between F 1 B and F 2 B is a right angle, then the square of the eccentricity of the ellipse is

Question

Aicharya · Accepted Answer

In standard ellipse x 2 a 2 + y 2 b 2 = 1 Semi-major axis O A = a Semi-minor axis O B = b Focus F 1 &#8801; - a e , 0 F 2 &#8801; a e , 0 &#8736; F 1 B F 2 = 9 0 &#176; O F 1 = O F 2 &#8658; &#8736; F 1 B O = &#8736; F 2 B O = 4 5 &#176; &#8658; a e b = tan 4 5 &#176; = 1 &#8658; b = a e Also, b 2 = a 2 1 - e 2 &#8658; a 2 e 2 = a 2 1 - e 2 &#8658; 2 e 2 = 1 &#8658; e 2 = 1 2

If O B is the semi-minor axis of an ellipse, F 1 and F 2 are its focii and the angle between F 1 B and F 2 B…

Solution