Question

graph each equation.

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

Explanation:

Identify the standard form parameters

$$
LATEXBLOCK0
$$

Determine key features of the ellipse

$$
LATEXBLOCK1
$$

Sketch the curve

$$ \text{An ellipse centered at } (0,0) \text{ with horizontal semi-axis } 2 \text{ and vertical semi-axis } 3. $$

Answer:

The equation represents an ellipse centered at the origin \((0,0)\).

The key features to graph are:

• Center: \((0,0)\)
• Horizontal intercepts (vertices on x-axis): \((2,0)\) and \((-2,0)\)
• Vertical intercepts (vertices on y-axis): \((0,3)\) and \((0,-3)\)