Question

graph each equation.

1. \frac{x^2}{4} + \frac{y^2}{9} = 1

Explanation:

Identify the ellipse parameters

Using the Standard Form of Ellipse knowledge point

$$
LATEXBLOCK0
$$

Determine key graphing points

Using the Graphing Ellipses knowledge point

$$
LATEXBLOCK1
$$

Answer:

The graph of the equation \(\frac{x^2}{4} + \frac{y^2}{9} = 1\) is a vertical ellipse centered at the origin \((0,0)\).

Its key boundary points are:

• Horizontal vertices (co-vertices): \((2, 0)\) and \((-2, 0)\)
• Vertical vertices (major vertices): \((0, 3)\) and \((0, -3)\)