QuestionAnalyze the equation. That is, find the center, vertices, and foci of the ellipse and graph it. $$\frac{x^{2}}{16}+\frac{y^{2}}{36}=1$$

Studdy Solution
Graph the ellipse:
1. Plot the center at $(0, 0)$.
2. Plot the vertices at $(0, 6)$, $(0, -6)$, $(4, 0)$, and $(-4, 0)$.
3. Plot the foci at $(0, 2\sqrt{5})$ and $(0, -2\sqrt{5})$.
4. Draw the ellipse passing through the vertices, ensuring it is elongated along the $y$-axis.
The center is $(0, 0)$, vertices are $(0, 6)$, $(0, -6)$, $(4, 0)$, $(-4, 0)$, and foci are $(0, 2\sqrt{5})$, $(0, -2\sqrt{5})$.