SOLUTION: find the equation of the graph of all points such that the difference of their distances from (4,0) and (-4,0) is always equal to 2.

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Question 1030970: find the equation of the graph of all points such that the difference of their distances from (4,0) and (-4,0) is always equal to 2.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let (x,y) be a point on the curve.
Then sqrt%28%28x%2B4%29%5E2+%2B+y%5E2%29+-+sqrt%28%28x-4%29%5E2+%2B+y%5E2%29+=+2
==> sqrt%28%28x%2B4%29%5E2+%2B+y%5E2%29+=+sqrt%28%28x-4%29%5E2+%2B+y%5E2%29+%2B+2
==> , after squaring both sides...
==> 4x+-+1+=+sqrt%28%28x-4%29%5E2+%2B+y%5E2%29, after reducing further..
==> 16x%5E2+-+8x+%2B1+=+x%5E2+-+8x%2B16+%2By%5E2 after squaring both sides.
==> 15x%5E2+-+y%5E2+=+15
==> x%5E2+-+y%5E2%2F15+=+1, which is a hyperbola center at (0,0) and x-axis as transverse axis.