Q: How is an ellipse different from a circle?

A circle is a special case of an ellipse where a=b=r. An ellipse has the equation x²/a²+y²/b²=1 with a≠b. It has two axes of symmetry of different lengths.

Q: What is a hyperbola?

A hyperbola is the curve x²/a²−y²/b²=1. It consists of two branches and has two asymptotes: y=±(b/a)x. The graph of y=k/x is a rectangular hyperbola.

Question 1

What is a parabola?

Accepted Answer

A parabola is the graph of a quadratic function y=ax²+bx+c. The vertex is at x₀=−b/(2a), y₀=f(x₀). If a>0 the parabola opens upward; if a<0 it opens downward.

Question 2

How is an ellipse different from a circle?

Accepted Answer

A circle is a special case of an ellipse where a=b=r. An ellipse has the equation x²/a²+y²/b²=1 with a≠b. It has two axes of symmetry of different lengths.

Question 3

What is a hyperbola?

Accepted Answer

A hyperbola is the curve x²/a²−y²/b²=1. It consists of two branches and has two asymptotes: y=±(b/a)x. The graph of y=k/x is a rectangular hyperbola.

Parabola, Ellipse, Hyperbola

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