Question

graph each equation.

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

Explanation:

Step1: Identify ellipse standard form

The given equation $\frac{x^2}{4} + \frac{y^2}{9} = 1$ matches the vertical ellipse standard form $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$ where $a > b$.

Step2: Calculate semi-axes lengths

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

Step3: Find key intercept points

• x-intercepts: $(\pm b, 0)=(\pm 2, 0)$
• y-intercepts: $(0, \pm a)=(0, \pm 3)$

Step4: Plot and connect points

Mark the intercepts $(-2,0),(2,0),(0,3),(0,-3)$ on the grid, then draw a smooth closed curve through these points to form the ellipse.

Answer:

The graph is a vertical ellipse centered at the origin $(0,0)$ with x-intercepts at $(\pm 2, 0)$ and y-intercepts at $(0, \pm 3)$, drawn as a smooth closed curve through these points on the provided coordinate grid.