SOLUTION: Determine the co-vertices (c-v) for the ellipse provided 2x(x + 5) = 10x + 8 - y^2 .

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Question 858195: Determine the co-vertices (c-v) for the ellipse provided 2x(x + 5) = 10x + 8 - y^2 .
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Calculate into standard form.
2x%5E2%2B10x=10x%2B8-y%5E2
2x%5E2=8-y%5E2
2x%5E2%2By%5E2=8
highlight%28x%5E2%2F4%2By%5E2%2F8=1%29

The "main" vertices are on the y-axis, so the minor vertices are on the x-axis. This ellipse has center on the origin. This is known because the denominators of 8 and 4 are of the order 4%3C8. The larger denominator identifies the major axis. The minor axis is also the one which contains the co-vertices. Your example has sqrt%284%29 or 2 for the distance from center to either co-vertex, so the co-vertices are (-2,0) and (2,0).