khally92
  • khally92
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ganeshie8
  • ganeshie8
Let \(P=(x,y,z)\) be any point on the required surface
ganeshie8
  • ganeshie8
remember the distance formula in 3D ?
khally92
  • khally92
yes

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khally92
  • khally92
I KNOW THE DISTANCE FORMUL IN 3D
ganeshie8
  • ganeshie8
Let M = (1,4,6) and N = (2,4,0) .
ganeshie8
  • ganeshie8
PM = 2*PN
ganeshie8
  • ganeshie8
use distance formula
khally92
  • khally92
you mean {(1-x )^2+( 4-y)^2 + (6-z)^2}^1/2=2PN
ganeshie8
  • ganeshie8
Yes
ganeshie8
  • ganeshie8
squaring both sides gets rid of radicals : \[(x-1)^2+(y-4)^2+(z-6)^2 = 4[(x-2)^2+(y-4)^2+(z-0)^2]\]
ganeshie8
  • ganeshie8
try simplifying
khally92
  • khally92
Ok thank you, I got 2x-12z+33=0 I will check my work again thank you so much really appreciate.
ganeshie8
  • ganeshie8
you should get a sphere
ganeshie8
  • ganeshie8
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
khally92
  • khally92
Awesome thank you, forgot to multiplied the right side by 4. thank you.
ganeshie8
  • ganeshie8
np :)

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