Question

graph each equation.

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

Explanation:

Step1: Identify ellipse standard form

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

Step2: Find $a$ and $b$ values

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

Step3: Locate vertices and co-vertices

Major vertices: $(0, \pm a)=(0, 3),(0, -3)$
Co-vertices: $(\pm b, 0)=(2, 0),(-2, 0)$

Step4: Plot points and draw ellipse

Connect the 4 points with a smooth, closed curve.

Answer:

The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing through these four points.