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

##### 1 Answer

The reference for Conic Section - General Cartesian form tells you how to determine what conic section it is.

#### Explanation:

The reference for Conic Section - General Cartesian form tells you how to determine what conic section it is, when given the General Cartesian form:

Here is the given equation in the general form:

Please observe the value of

Divide both sides of the original equation by 8:

Write the denominators as squares:

Insert zeros within the squares in the numerators:

This is the standard form for an ellipse, because it is easy to see:

- The center is (0, 0)
- When
#y = 0, x = -2 and 2# - When
#x = 0, y = -sqrt(2) and sqrt(2)#

You may use these four points to graph the equation:

And then sketch in an ellipse around the center.

Here is a graph of the equation: