Question

graph each equation.

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

Explanation:

Identify key features of the ellipse

$$
LATEXBLOCK0
$$

Determine the key plotting points

$$
LATEXBLOCK1
$$

Answer:

To graph the equation \(\frac{x^2}{4} + \frac{y^2}{9} = 1\), plot the key points of the ellipse centered at the origin \((0,0)\):

• Vertices on the \(y\)-axis: \((0, 3)\) and \((0, -3)\)
• Co-vertices on the \(x\)-axis: \((2, 0)\) and \((-2, 0)\)

Draw a smooth, symmetric oval passing through these four points.