The ellipse looks like this:
The general format of a vertical ellipse takes the form:
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}[/tex]With center coordinates as (h,k)
By comparing the equation given:
[tex]\frac{(x-6)^2}{36}+\frac{(y+3)^2}{100}=1[/tex][tex]\begin{gathered} -h=-6 \\ h=6 \\ -k=+3 \\ k=-3 \\ \text{The center is (6,-3)} \end{gathered}[/tex]The endpoints of the major axis are 10 units from the center.
The endpoints of the minor axis are 6 units from the center.
To graph the ellipse, connect (12,-3) , (6,-13) , (0,-3) , (6,7) with a smooth curve.
