using algebra, that the formula for a circle is a special case of

Show, using algebra, that the formula for a circle is a special case of
the formula for an ellipse.

2. Show, using algebra, that the formula for a parabola is a special case
of the formula for an ellipse.
3. In the context of a parabola, what is a focus? What is a directrix?
What are the advantages of expressing the equation of a parabola in
focus-directrix form?
4. What happens to the shape of a parabola, as the distance between the
vertex of the curve and the focus becomes very large? Prove your answer
using algebra.

Show, using algebra, that the formula for a circle is a special case of
the formula for an ellipse.