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

1 Answer

Feb 24, 2016

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

Explanation:

Transformed into standard elliptical form:
$XXX \frac{x^{2}}{3^{3}} + \frac{y^{2}}{2^{2}} = 1$ $color(white)("XXX")x^2/3^3+y^2/2^2=1$

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

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

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