Question

graph each equation.

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

Explanation:

Identify key parameters of the ellipse

$$
LATEXBLOCK0
$$

Determine key plotting points

$$
LATEXBLOCK1
$$

Sketch the ellipse

$$ \text{Draw a smooth vertical ellipse centered at } (0,0) \text{ passing through } (0,3), (0,-3), (2,0), \text{ and } (-2,0). $$

Answer:

To graph the equation \(\frac{x^2}{4} + \frac{y^2}{9} = 1\):

1. Center: \((0, 0)\)
2. Vertices (vertical axis): \((0, 3)\) and \((0, -3)\)
3. Co-vertices (horizontal axis): \((2, 0)\) and \((-2, 0)\)

Plot these four points on the coordinate plane and connect them with a smooth, symmetric oval shape to form the ellipse.