Finding the Equation for the Plane of Equidistant Points: Solving for b and c

[Mary89]

Homework Statement

Find an equation for the plane consisting of all points that are equidistant from the points

(1,0,-2) and (3,4,0)

Homework Equations

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

 

[genneth]

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?

 

[dynamicsolo]

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.