Question

graph each equation.

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

Explanation:

Identify the conic section parameters

$$
LATEXBLOCK0
$$

Determine key vertices

$$
LATEXBLOCK1
$$

Sketch the ellipse

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

Answer:

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

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

To graph the equation, plot these four points on the coordinate plane and connect them with a smooth, symmetric oval curve.