Question

graph the ellipse.
9x² + 4y² = 36

Explanation:

Step1: Rewrite the equation in standard form

Divide the given equation $9x^{2}+4y^{2}=36$ by 36. We get $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$.

Step2: Identify the center, semi - axes

For an ellipse of the form $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}} = 1$ (where $a>b>0$), the center is at the origin $(0,0)$. Here $a = 3$ and $b = 2$. The vertices on the major axis (along the y - axis since $a = 3$) are $(0,3)$ and $(0, - 3)$, and the vertices on the minor axis are $(2,0)$ and $(-2,0)$.

Step3: Sketch the ellipse

Plot the center at the origin, the vertices $(0,3),(0, - 3),(2,0),(-2,0)$ and then draw a smooth curve to form the ellipse.

Answer:

Sketch an ellipse centered at the origin with vertices $(0,3),(0, - 3),(2,0),(-2,0)$