Question 1193860
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Find the general equation of the ellipse whose major axis is 20 units and the foci are
the points of coordinates (0, 5√3) and (0, −5√3).
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<pre>
From the post, the ellips has the center at point (0,0), which is the origin of the coordinaste system.

Foci are located at y-axis.


It means that the major axis lies on vertical y-axis.


The major axis is 20 units long; hence, the major semi-axis is a = 10 units long.


The eccentricity (the distance from the center to each foci) is  c = {{{5*sqrt(3)}}}.


It means that the minor semi-axis is  

    b = {{{sqrt(a^2 - c^2)}}} = {{{sqrt(100-(5*sqrt(3))^2)}}} = {{{sqrt(100-25*3)}}} = {{{sqrt(25)}}} = 5.


Now the general equation of the ellipse is

    {{{y^2/10^2}}} + {{{x^2/5^2}}} = 1.    <U>ANSWER</U>
</pre>

Solved.


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To understand in full what is written in the post, &nbsp;see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-definition--canonical-equation--characteristic-points-and-elements.lesson>Ellipse definition, canonical equation, characteristic points and elements</A> 

in this site.