Ellipse Quiz

Put the following four equations in standard form, find the vertices of the major and minor axes and foci for each ellipse, and graph the ellipse.

1. 2x² + 12y² = 6
2. -3x² + 4y² - 12 = 0
3. x² + 2y² - 10x + 8y = -29
4. 3x² + 18x + 3y² - 24y = 16

Use the information given in the next four problems to construct an equation of an ellipse in standard form and graph the ellipse.

1. The endpoints of the major axis are at (0,7) and (0,-7). The foci are at (0,-4) and (0,4).
2. The foci are at (2,5) and (2,10) and the length of the major axis is 10.
3. The endpoints of the minor axis are at (-2,6) and (-2,0) and the endpoints of the major axis are at (-8,3) and (4,3).
4. 

And the last problem,

The elliptical orbit of the planet Jupiter has the center of the sun as one focus. If the closest distance to the center of the sun is 460 million miles and the farthest distance is 508 million miles, how far from the center of the sun is the second focus?

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