SOLUTION: Find an equation such that the distance between (x,y) and (3,5) is twice that of (-2,-4) Please help!! Thanks

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Question 785424: Find an equation such that the distance between (x,y) and (3,5) is twice that of (-2,-4)
Please help!!
Thanks
Answer by Menjax(62) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation such that the distance between (x,y) and (3,5) is twice that of (-2,-4)
Interpretation:
Find an equation that describes all the points that are spaced twice the distance between (-2,-4) and (3,5) from (3,5). In other words find a circle with radius of twice the distance between (-2,-4) and (3,5).
Find the distance between (-2,-4) and (3,5):
Using the distance formula distance+=+sqrt%28%28dx%29%5E2%2B%28dy%29%5E2%29
D+=+sqrt%28%28-2-3%29%5E2%2B%28-4-5%29%5E2%29
D+=+sqrt%28%28-5%29%5E2%2B%28-9%29%5E2%29
D+=+sqrt%28106%29
Seeing that the points are double the distance away, the radius of the circle is 2d which means the equation describing the points is
%282D%29%5E2=%28x-3%29%5E2%2B%28y-5%29%5E2
+4D%5E2=%28x-3%29%5E2%2B%28y-5%29%5E2
+%28x-3%29%5E2%2B%28y-5%29%5E2+=+424
explaination
any point on this line is twice the distance between(3,5) and (-2,-4) from the centre (3,5)