Question

graph each equation.

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

Explanation:

Step1: Identify ellipse type

The equation is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ where $a^2=4$, $b^2=9$. Since $b>a$, it's a vertical ellipse.

Step2: Find vertices

$a=\sqrt{4}=2$, $b=\sqrt{9}=3$.
x-intercepts: $(\pm2,0)$; y-intercepts: $(0,\pm3)$

Step3: Plot points and draw

Mark $(\pm2,0)$ and $(0,\pm3)$, then sketch the ellipse through these points.

Answer:

An ellipse centered at the origin with vertices at $(\pm2,0)$ and $(0,\pm3)$ (graph drawn through these points).