Question

Can someone please help me figure out how to set up this problem? Consider the points P such that the distance from P to A(-1, 5, 3) is twice the distance from P to B(6, 2, -2). Show that the set of all such points is a sphere, and find its center and radius.

Answer 1

Use the distance formula
Let point P be (x,y,z)
\[\sqrt{(x+1)^{2}+(y-5)^{2}+(z-3)^{2}} = 2*\sqrt{(x-6)^{2}+(y-2)^{2}+(z+2)^{2}}\]
square both sides
\[(x+1)^{2}+(y-5)^{2}+(z-3)^{2} = 4*((x-6)^{2}+(y-2)^{2}+(z+2)^{2})\]
Combine like terms on one side, put constants on other side
Use completing the square to get it in standard form
\[(x-\frac{25}{3})^{2}+(y-1)^{2}+(z+\frac{11}{3})^{2} = \frac{1178}{9}\]

Answer 2

correction, right side should be (332/9)

Answer 3

thanks so much!

Answer 4

your welcome