Find an equation of the set of all points equidistant from the points A (-2,3,7) and B (9,1,-7).?

Question

22x-4y-28z=69

didn't understand how it works because after inserting any points back into the equation it doesn't equal 69.

Answer 1

You need to minimize the distance between the two points.

|P1P2| = sqrt[ (x2 -x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]

You can remove the sqrt because it is on both sides.

(x+2)^2 + (y-3)^2 + (z-7)^2 = (x-9)^2 + (y-1)^2 + (z+7)^2

Multiplying Out

x^2 + 4x + 4 +y^2 - 6y + 9 + z^2 -14z +49 = x^2 -18x + 81 + y^2 +14y +49 + z^2 + 14z + 49

Simplifying

22x - 4y - 28z = 69