Question

If the angle between the lines joining the focii to an extremity of the minor axis of an ellipse is 90, then its eccentricity is:

a. 0
b. 0.5
c. 1
d. √2/2

Answer 1

The eccentricity of the ellipse is 1.

Step-by-step explanation:

The eccentricity (e) of an ellipse can be calculated by dividing the distance (f) from the center of the ellipse to one of the foci by half the length of the major axis (a). The angle between the lines joining the foci to an extremity of the minor axis of the ellipse being 90 degrees indicates that the distance between the foci is equal to the length of the major axis. Therefore, the eccentricity can be calculated as follows:

e = f / a = a / a = 1

Thus, the eccentricity of the ellipse is 1, which corresponds to option c.