Question

How do I write an equation to describe this graph?

Answer 1

From the given picture, we can to note that the major axis is located on the x-axis. So, the ellipse equation has the form

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

where (h,k) is the coordinate of the center, a is the distance from the center one vertex (the one located on the major axis) and b is the distance from the center to the minor axis vertex, that is,

Then, from the picture above, we can note that

$\begin{gathered} a=6 \\ b=4 \\ (h,k)=(0,0) \end{gathered}$

So, by substituting these values into our first equation, we get

$\frac{(x-0)^2}{6^2}+\frac{(y-0)^2}{4^2}=1$

Therefore, the answer the ellipse equation is:

$\frac{x^2}{36}+\frac{y^2}{16}=1$