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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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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 = = = = 4 units.
The canonical equation of this ellipse is
+ = 1. ANSWER
Solved.
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On canonical equation for ellipses, see the lesson
- Ellipse definition, canonical equation, characteristic points and elements
in this site.