### All High School Math Resources

## Example Questions

### Example Question #3 : Conic Sections

A conic section is represented by the following equation:

What type of conic section does this equation represent?

**Possible Answers:**

Circle

Parabola

Ellipse

Hyperbola

**Correct answer:**

Hyperbola

Explanation:

The simplest way to know what kind of conic section an equation represents is by checking the coefficients in front of each variable. The equation must be in general form while you do this check. Luckily, this equation is already in general form, so it's easy to see. The general equation for a conic section is the following:

Assuming the term is 0 (which it usually is):

- If
*A*equals*C*, the equation is a circle. - If
*A*and*C*have the same sign (but are not equal to each other), the equation is an ellipse. - If either
*A*or*C*equals 0, the equation is a parabola. - If
*A*and*C*are different signs (i.e. one is negative and one is positive), the equation is a hyperbola.