Question

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.?

Answer 1

`4x^2+9y^2=36` is an ellipse

Explanation:

Transformed into standard elliptical form:
`color(white)("XXX")x^2/3^3+y^2/2^2=1`

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

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