Question

Find an equation in simplified form for the set of all points whose
distance to (1,4,6) is twice the distance to (2,4,0) .
Name and give a precise description of this surface

Help Please.

Answer 1

Let \(P=(x,y,z)\) be any point on the required surface

Answer 2

remember the distance formula in 3D ?

Answer 3

yes

Answer 4

I KNOW THE DISTANCE FORMUL IN 3D

Answer 5

Let M = (1,4,6) and N = (2,4,0) .

Answer 6

PM = 2*PN

Answer 7

use distance formula

Answer 8

you mean {(1-x )^2+( 4-y)^2 + (6-z)^2}^1/2=2PN

Answer 9

Yes

Answer 10

squaring both sides gets rid of radicals : \[(x-1)^2+(y-4)^2+(z-6)^2 = 4[(x-2)^2+(y-4)^2+(z-0)^2]\]

Answer 11

try simplifying

Answer 12

Ok thank you,
I got 2x-12z+33=0

I will check my work again

thank you so much

really appreciate.

Answer 13

you should get a sphere

Answer 14

http://www.wolframalpha.com/input/?i=simplify+%28x-1%29%5E2+%2B+%28y-4%29%5E2+%2B+%28z-6%29%5E2+%3D+4%28%28x-2%29%5E2%2B%28y-4%29%5E2%2B%28z-0%29%5E2%29

Answer 15

Awesome thank you, forgot to multiplied the right side by 4.

thank you.

Answer 16

np :)