Question 1177760
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Find an equation of the set of points on a plane such that the sum of the distances 
between each point of the set and the points (0,3) and (0,-3) is 10 units.
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<pre>
This set of points is the ellipse on a coordinate plane, centered at the origin

and having focuses at given points (0,3)  and  (0,-3).


Its major axis is vertical; minor axis is horizontal;


the major semi-axis "a" has the length 

    (a-3) + (a-(-3)) =10,  or, equivalently,  (a-3) + (a+3) = 10,  2a = 10,  a = 5 units.


The minor semi-axis "b" has the length  b = {{{sqrt(a^2-c^2)}}} = {{{sqrt(5^2-3^2)}}} = {{{sqrt(16)}}} = 4 units.


The canonical equation of this ellipse is


    {{{X^2/4^2}}} + {{{y^2/5^2}}} = 1.      <U>ANSWER</U>
</pre>

Solved.


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On canonical equation for ellipses, 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.