SOLUTION: Find an equation for the collection of points for which the distance to (18, 0) is twice the distance to the line x = -18.

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Question 1149941: Find an equation for the collection of points for which the distance to (18, 0) is twice the distance to the line x = -18.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


Let (x,y) be an arbitrary point on the curve of points in the collection.
We use the distance formula to find



That is the equation:

sqrt%28%28x-18%29%5E2%2B%28y-0%29%5E2%29=2sqrt%28%28x%2B18%29%5E2%2B%28y-y%29%5E2%29

Simplify and get

y%5E2-3x%5E2-180x-972+=+0

which is a hyperbola with vertex (-6,0), but we only need the right 
branch, for the distance to the left branch would be more than twice
the distance from (18,0), so we should put an inequality to rule out 
the left branch of the hyperbola:

matrix%281%2C2%2Cy%5E2-3x%5E2-180x-972+=+0%2Cx%3E=6%29

Edwin