Question

graph each equation.

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

Explanation:

Step1: Identify ellipse standard form

The equation $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ (vertical major axis, $a>b$) matches $\frac{x^2}{4}+\frac{y^2}{9}=1$.

Step2: Find $a$ and $b$ values

$a^2=9 \implies a=3$, $b^2=4 \implies b=2$

Step3: Locate vertices and co-vertices

• Vertices (y-axis): $(0, \pm a)=(0,3), (0,-3)$
• Co-vertices (x-axis): $(\pm b, 0)=(2,0), (-2,0)$

Step4: Plot points and draw ellipse

Connect the plotted points with a smooth, closed curve.

Answer:

The graph is a vertical ellipse with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, drawn as a smooth closed curve through these points on the provided coordinate grid.