# How do you classify the conic #4x^2-y^2-8x+4y-9=0#?

##### 2 Answers

It is a hyperbola.

#### Explanation:

or

or

As

graph{4x^2-y^2-8x+4y-9=0 [-9.46, 10.54, -3.76, 6.24]}

The General Cartesian form for a conic section is:

One may use the value of

#### Explanation:

The given equation

Fits the General Cartesian form with

Refering to the reference section entitled, Discriminant , we compute the value:

The value is greater than zero. The list of conditions given by reference tells us that the conic section is a hyperbola.