The general equation of the ellipse is as follows:
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]
where (h, k) is the center of the ellipse.
Thus, the center of the given ellipse is (6,-3).
The endpoints of the major axis is given by the following expression:
[tex](h,k\pm a)[/tex]
From the given equation, the value of a² is 100. Thus, the value of a is 10.
Substitute the value of h, k, and a into the coordinates of the endpoints of the major axis.
[tex](h,k\pm a)=(6,-3\pm10)[/tex]
Thus, the endpoints of the major axis are (6,7) and (6,-13).
This means that the endpoints of the major axis is 10 units away from the center.
On the other hand, the endpoints of the minor axis is b units away from the center. The value of b can be obtained from the equation.
Since b² is 36, the value of b must be 6. Thus, the endpoints of the minor axis is 6 units away from the center.
To graph the ellipse, the endpoints of the minor and major axes must be connected with a smooth curve.
To obtain the endpoints of the minor axis, substitute h, k, and b into the following coordinates.
[tex](h\pm b,k)=(6\pm6,-3)[/tex]
Thus, the endpoints of the minor axes are (0,-3) and (12,-3).
Finally, to graph the ellipse, draw a smooth curve passing through the endpoints of the major and minor axes: (6,7), (6,-13), (0,-3) and (12,-3).
