Question

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

Answer 1

Answer:

Ellipse

Step-by-step explanation:

Given the equation

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

Divide this equation by 36:

$\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=\dfrac{36}{36}\\ \\ \\\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$

The equation of the form

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

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