Question

graph each equation.

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

Explanation:

Identify the conic section

Using the Standard Form of Ellipse knowledge point

$$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $$

$$ \frac{x^2}{4} + \frac{y^2}{9} = 1 \implies a^2 = 4, \ b^2 = 9 $$

Find key features of the ellipse

Using the Graphing Ellipses knowledge point

$$
LATEXBLOCK0
$$

Plot key points and sketch

Using the Graphing Ellipses knowledge point

$$
LATEXBLOCK1
$$

Answer:

To graph the equation \(\frac{x^2}{4} + \frac{y^2}{9} = 1\), plot the key points of the ellipse and draw a smooth curve connecting them:

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