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Write the equation of an ellipse with a major axis of length 8 and co-vertices (0, 3)...

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cstavro

Posted August 28, 2013 at 11:44 PM via web

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Write the equation of an ellipse with a major axis of length 8 and co-vertices (0, 3) and (0, -3).

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted August 29, 2013 at 1:03 AM (Answer #1)

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The general form for an ellipse is `x^2/a^2+y^2/b^2=1` , assuming the ellipse is centered at the origin. If a>b the major axis is horizontal, if a<b the major axis is vertical.

The vertices lie along the major axis. If a>b they are (a,0),(-a,0).

The covertices lie on the minor axis; if a>b then they are (0,b),(0,-b).

We are given the covertices as (0,3) and (0,-3) so the major axis is horizontal. From this we get b=3.

The length of the major axis is 2a -- since the length is 8 we have a=4.

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The equation is `x^2/16+y^2/9=1`

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The graph:

 

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