Eccentricity Of A Conic

We are given that the angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is . This condition is used to determine the eccentricity of the ellipse.
Step 1: Recall the geometry of an ellipse.
For an ellipse, the foci are located along the major axis, and the distance between the foci is , where is the focal distance. The semi-major axis is , and the semi-minor axis is . The eccentricity is
given by:
The angle between the lines joining the foci to one particular extremity of the minor axis is related to the eccentricity .
Step 2: Use the condition on the angle.
The formula for the angle between the lines joining the foci to the extremity of the minor axis is: We are
given that , so:
which leads to the relationship: Solving this equation gives the eccentricity . Thus, the correct answer is .