# How do you know if the conic section #x^2 -9y^2 +36y -45= 0# is a parabola, an ellipse, a hyperbola, or a circle?

##### 1 Answer

Nov 12, 2015

Look at the coefficients on

#### Explanation:

The coefficient on

If the coefficients are different and also different signs (+ or -), then it must be hyperbola.

**Detailed Explanation:**

**EVERY** *conic section* can be written with the **general equation** :

Here is how you distinguish the various conic sections from the **coefficients** in the general equation:

**circle** :

**ellipse** : **SAME sign** (+ or -)

**hyperbola** : **DIFFERENT signs**

**parabola** : either A or B equals 0 (only **one squared term** in the equation)

hope that helped