If the eccentricity of an ellipse is zero, then show that it will be a circle.

Define eccentricity of an ellipse

The eccentricity of the ellipse

When the eccentricity of a ellipse becomes zero , then it becomes a

The eccentricity e of an ellipse satisfies the condition :

If the eccentricity is zero, show that the ellipse becomes a circle.

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is 1/2, then find the locus of the focus.

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is 1/2, then find the locus of the focus.