Question

graph each equation.

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

Explanation:

Step1: Identify the standard form of ellipse

The standard form of an ellipse is $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}} = 1$ ($a>b>0$), where the major - axis is along the $y$ - axis, vertices are $(0,\pm a)$ and co - vertices are $(\pm b,0)$.
For the equation $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$, we have $b^{2} = 4$ (so $b = 2$) and $a^{2}=9$ (so $a = 3$).

Step2: Find the vertices and co - vertices

The vertices (end - points of the major axis) are $(0,\pm a)=(0,\pm3)$.
The co - vertices (end - points of the minor axis) are $(\pm b,0)=(\pm2,0)$.

Step3: Plot the points and draw the ellipse

Plot the points $(0,3),(0, - 3),(2,0),(-2,0)$ on the coordinate plane. Then sketch the ellipse passing through these four points.

Answer:

Plot the vertices $(0,3)$ and $(0, - 3)$ (along the $y$ - axis) and co - vertices $(2,0)$ and $(-2,0)$ (along the $x$ - axis) and draw the ellipse passing through these four points.