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 major axis ellipse standard form $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$ where $a > b$.

Step2: Find $a$, $b$ values

Compare denominators: $a^2=9 \implies a=3$, $b^2=4 \implies b=2$.

Step3: Locate vertices/co-vertices

• Vertical vertices: $(0, \pm a) = (0, 3), (0, -3)$
• Horizontal co-vertices: $(\pm b, 0) = (2, 0), (-2, 0)$

Step4: Plot points and draw ellipse

Plot the 4 points, then sketch a smooth closed curve through them.

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.