# How do you identity if the equation #3x^2+4y^2+8y=8# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 1 Answer

Nov 19, 2016

This is an ellipse

#### Explanation:

Compare this to the general equation for conics and calculate the discriminant.

The discriminant is

if

If

If

In our case,

so,

We can also, rearrage the equation

Dividing by 12

which is an equation of an ellipse

The center is

The foci are F

The major axis is

and the minor axis is

graph{(3x^2+4y^2+8y-8)(y-1)=0 [-4.915, 3.855, -3.362, 1.023]}