Final answer:
The equation in standard form for the ellipse is x^2/a^2 + y^2/b^2 = 1. The coordinates for the center are (0, 0). The foci points are calculated using the formula c = sqrt(a^2 - b^2), and the major and minor axis lengths are represented by 2a and 2b respectively.
Step-by-step explanation:
1. The equation in standard form for the ellipse can be written as x2/a2 + y2/b2 = 1, where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.
2. The coordinates for the center of the ellipse are (0, 0) since the ellipse is centered at the origin.
3. The coordinates of the two foci points can be calculated using the formula c = sqrt(a2 - b2), where 'c' represents the distance from the center to each focus. Therefore, the coordinates of the two focus points are (c, 0) and (-c, 0).
4. The major axis length of the ellipse is represented by '2a'. To find this length, we measure the distance from one end of the ellipse to the other end along the major axis. 'a' is also the distance from the center to either side of the ellipse along the x-axis.
5. The minor axis length of the ellipse is represented by '2b'. To find this length, we measure the distance from one end of the ellipse to the other end along the minor axis. 'b' is also the distance from the center to either side of the ellipse along the y-axis.
6. The ellipse may be different from others in the class based on the size and proportions of the axes, as well as the position of the center and foci.
7. The ellipse may be similar to others in the class if they share the same proportions of the major and minor axis lengths, have their centers at the origin, and have the same distance between the foci and the major axis.