# How do you classify 4x^2 + 9y^2 = 36?

Sep 1, 2015

This equation represents an ellipse

#### Explanation:

An ellipse is 2-dimensional figure that, to me, looks more like a stretched circle.

$4 {x}^{2} + 9 {y}^{2} = 36 \text{ }$ is the equation of an ellipse as it can be written in the form:

${\left(x - h\right)}^{2} / {a}^{2} + {\left(x - k\right)}^{2} / {b}^{2} = 1 \text{ }$ which is the general form of an ellipse!

Like this:

4x^2+9y^2=36 color(red)rarr (4x^2)/36+(9y^2)/36=1 color(red)rarr x^2/(9)+y^2/(4)=1 color(red)rarr x^2/(3)^2+y^2/(2)^2=1color(red)

graph{(4x^2+9y^2-36)=0 [-10, 10, -5, 5]}