Finding an equation for an ellipse
- Thread starter sareen
- Start date
Ellipses are easy to deal with. Since one vertex is at (-2,-4) and another at (-2,6), that means the distance from one vertex
to the other is 10 units. Therefore, it is 5 units from the center to each vertex. Therefore, the center is at (-2,1).
It is 3 units from the center to the focus, so the minor axis has length \(\displaystyle \sqrt{5^{2}-3^{2}}=4\) units on each side of
the center. The other focus is at (-2,4). See?. 6 units between the foci.
The major axis is parallel to the y-axis, so we have
\(\displaystyle \frac{(x+2)^{2}}{16}+\frac{(y-1)^{2}}{25}=1\)
Graph it an see. Casio makes a calculator that graphs conics by entering in the center coordinates and the lengths of the
respective axes. But with most, we have to solve for y. Doing this gives us the ellipse. The foci are the red asterisks.
to the other is 10 units. Therefore, it is 5 units from the center to each vertex. Therefore, the center is at (-2,1).
It is 3 units from the center to the focus, so the minor axis has length \(\displaystyle \sqrt{5^{2}-3^{2}}=4\) units on each side of
the center. The other focus is at (-2,4). See?. 6 units between the foci.
The major axis is parallel to the y-axis, so we have
\(\displaystyle \frac{(x+2)^{2}}{16}+\frac{(y-1)^{2}}{25}=1\)
Graph it an see. Casio makes a calculator that graphs conics by entering in the center coordinates and the lengths of the
respective axes. But with most, we have to solve for y. Doing this gives us the ellipse. The foci are the red asterisks.
