## Finding the equation of an ellipse

Geometric formulae, word problems, theorems and proofs, etc.
dorislouise
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### Finding the equation of an ellipse

Find the equation of an ellipse given vertices (0, 4) and (0, -4) and which passes through the point (-1,3)

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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You are given the vertices of the ellipse, which are eight units apart on the y-axis, and centered on the origin. So you know that, in the ellipse equation:

. . . . .$\frac{(y\, -\, k)^2}{a^2}\, +\, \frac{(x\, -\, h)^2}{b^2}\, =\, 1$

...the value of "a" is 4, and (h, k) = (0, 0). You are given a point on the ellipse. Plug the x- and y-values from this point into the equation, along with the other known values, and solve for the one remaining value.