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Is this an ellipsoid?by Mary89
Tags: ellipsoid 
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#1
Sep2907, 05:09 PM

P: 4

1. The problem statement, all variables and given/known data
Find an equation for the plane consisting of all points that are equidistant from the points (1,0,2) and (3,4,0) 2. Relevant equations 3. The attempt at a solution I found the midpoint ant (4, 4, 2), which I believe is the center. However, I have no idea on how to find a b and c. So that my equation looks like an ellipsoid... Help pleaseee 


#2
Sep2907, 05:30 PM

P: 981

It asks for a the equation of a plane. I'd try to find a plane  which does not have a centre. Remember all the different ways to specify a plane in 3D? Remember the one about a normal and a point on the plane? How might you construct the normal to the plane and a point on it?



#3
Sep3007, 12:53 AM

HW Helper
P: 1,663

As to your question, the ellipsoid would be the set of points such that the sum of the distance from a point on the ellipsoid to one of the given points and the distance from that point of the ellipsoid to the other given point is constant. Your points (1,0,2) and (3,4,0) would be the foci of the ellipsoid.
For the problem, the plane would pass through the midpoint (4, 4, 2)/2 = (2, 2, 1) [you need to divide by 2], so that the points (1,0,2) and (3,4,0) would look like reflections of each other in a mirror. genneth's questions suggest how you would arrange that. 


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