# How do you identity if the equation #5x^2+6x-4y=x^2-y^2-2x# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 1 Answer

#### Answer:

It is an ellipse.

#### Explanation:

Let us write the equation in the form

As

or

Hence, here we have

and therefore

Hence it is an ellipse (for details see here).

The equation can be written as

or

or

Here, we have center at

graph{5x^2+6x-4y=x^2-y^2-2x [-11.75, 8.25, -2.84, 7.16]}