# How do you classify the conic #-2y^2+x+5y+26=0#?

##### 1 Answer

A parabola

#### Explanation:

Conics can be represented as

where

For conics

The characteristic polynomial is

Depending on their roots, the conic can be classified as

1) Equal --- circle

2) Same sign and different absolute values --- ellipse

3) Signs different --- hyperbole

4) One null root --- parabola

In the present case we have

with characteristic polynomial

with roots

Determining

giving