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
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?
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.