graph each equation.\n9) $\\frac{x^{2}}{4} + \\frac{y^{2}}{9} = 1$

Explanation:

Step1: Identify the conic section type

The equation $\frac{x^2}{4} + \frac{y^2}{9} = 1$ represents an ellipse centered at $(0,0)$.

Step2: Determine the semi-axes lengths

The denominators are $a^2 = 9$ and $b^2 = 4$, so $a = 3$ (vertical) and $b = 2$ (horizontal).

Step3: Identify the vertices and co-vertices

Vertices are at $(0, \pm 3)$ and co-vertices are at $(\pm 2, 0)$.

Step4: Sketch the ellipse through points

Plot $(0, 3), (0, -3), (2, 0), (-2, 0)$ and connect them with a smooth curve.

Answer:

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