What is the equation of the ellipse with foci (5, 0), (-5, 0) and co-vertices (0, 4), (0, -4)?

Asked on by emstavro

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Since the covertices are on the y-axis, the major axis is horizontal.

The equation is in the form `x^2/a^2+y^2/b^2=1` where 2a is the length of the major axis and 2b is the length of the minor axis. The foci are related to the vertices and covertices by `a^2-b^2=c^2` where c is the length fromthe center to the foci.

Here b=4 and c=5 so `a^2-16=25 ==> a^2=41`


The equation is `x^2/41+y^2/16=1`


The graph:

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