Question 173642: Find an equation of the ellipse that satisfies the given conditions.
Vertices are (+-5,0), foci (+-sqrt(21),0) Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! i think the following graph is it.
look below the graph for further comments.
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standard equation of a ellipse where the major axis is horizontal and the center of the ellipse is at the origin is:
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hard to explain but a decent treatment of this can be found at the following web address:
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_conics_ellipse.xml
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you are given:
vertices are: (+-5,0)
focii are: (+-sqrt(21),0)
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since the focii are on the x-axis, then this equation has a major axis as horizontal.
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this make a = 5, since the a is the distance from the horizontal vertex to the origin.
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we need to find b.
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use the equation
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c is the distance from the focus to the origin.
that would be sqrt(21)
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the equation is:
substituting:
b = 2
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we have:
a = 5
b = 2
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standard equation becomes:
to graph this solve for y:
that equation becomes:
y = +/-
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sorry for the rush job but i ran out of time.
hopefully this helps.
check that website out.
decent treatment of the subject.
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