If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:

Question

Aicharya · Accepted Answer

2 a e = 1 2 &#215; 2 b 2 a 2 e = b 2 a 2 We know that e = 1 - b 2 a 2 e = 1 - 2 e e 2 = 1 - 2 e e 2 + 2 e - 1 = 0 - 2 &#177; 4 + 4 2 = - 2 &#177; 2 2 2 - 1 + 2 &#160; &#160; &#38; &#160; - 1 - 2 &#8756; &#160; &#160; &#160; e = 2 - 1

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity…

Solution