Question

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

Answer 1

This equation represents an ellipse

Explanation:

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

`4x^2+9y^2=36" "` is the equation of an ellipse as it can be written in the form:

`(x-h)^2/a^2+(x-k)^2/b^2=1" "` 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]}