1. 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.