How do you identify the following equation 4x^2 + 9y^2 = 36 as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?

Feb 24, 2016

$4 {x}^{2} + 9 {y}^{2} = 36$ is an ellipse

Explanation:

Transformed into standard elliptical form:
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} / {3}^{3} + {y}^{2} / {2}^{2} = 1$

This is an ellipse with horizontal ($x$) axis $\left[- 3 , + 3\right]$
and vertical ($y$) axis $\left[- 2 , + 2\right]$

graph{4x^2+9y^2=36 [-4.933, 4.934, -2.465, 2.467]}