# How do you identity if the equation #7x^2-28x+4y^2+8y=-4# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 1 Answer

Please open this link General Cartesian Form in another tab and read, carefully.

#### Explanation:

From the reference, the General Cartesian Form is:

Rewriting the given equation in the form:

We observe that

Compute the discriminant:

According to the conditions described in the reference, the discriminant is less than zero, therefore, the equation describes an ellipse.

Because

Because

Factor a 7 out of the first 3 term and a 4 out of the next 3 terms:

Use the expansions of

and

to match the middle terms with the middle terms in equation [4]:

To find the value of h, use the equation:

To find the value of k, use the equation:

Substitute

Substitute -1 for k and 2 for h:

Divide both sides of the equation by 28:

Write the denominators as squares:

The center is

The major axis end points are

The minor axis end points are

Here is a graph: