##### What is vertex form equation of an ellipse?

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What is vertex form equation of an ellipse with center (0,9), and a major axis length of 10 and minor axis length of 4?

May 16th, 2015

The vertex form of an ellipse is; (x-h)^2/a^2 + (y-k)^2/b^2 = 1 or (x-h)^2/b^2 + (y-k)^2/a^2 = 1, with (h,k) being the center, and a and b being the major and minor axis' lengths in half. The form changes depending on which way the major axis has the longer length. So, in your case, it can be:

x^2/25 + (y-9)^2/4 = 1, or x^2/4 + (y-9)^2/25 = 1, depending on how the axis are. If the ellipse is more horizontal then vertical, then it is the first equation. If the ellipse is more vertical than horizontal, then it the second one. A is always the major axis' length cut in half.

May 17th, 2015

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May 16th, 2015
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May 16th, 2015
Oct 17th, 2017
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