Question

graph each equation.

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

Explanation:

Step1: Identify the ellipse type

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

Step2: Find a, b, center

$a^2=9\Rightarrow a=3$, $b^2=4\Rightarrow b=2$, center $(0,0)$.

Step3: Locate vertices and co-vertices

Vertices: $(0,\pm3)$; Co-vertices: $(\pm2,0)$.

Step4: Plot points and draw ellipse

Connect vertices and co-vertices smoothly.

Answer:

The graph is a vertical ellipse centered at the origin with vertices at (0, 3), (0, -3) and co-vertices at (2, 0), (-2, 0).