Question

Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola.

4x2 +9y2 = 36

Answer 1

Ellipse

Explanation:

Given the equation

`4x^2 +9y^2 =36`

Divide this equation by 36:

`(4x^2)/(36)+(9y^2)/(36)=(36)/(36)\\ \\ \\(x^2)/(9)+(y^2)/(4)=1`

The equation of the form

`(x^2)/(a^2)+(y^2)/(b^2)=1`

represents an ellipse, so given equation is the equation of the ellipse.