SOLUTION: Find a formula for the set of all points (x, y) for which the sum of the distances from (x, y) to (4, 0) and from (x, y) to (-4, 0) is 10.

Algebra ->  Coordinate-system -> SOLUTION: Find a formula for the set of all points (x, y) for which the sum of the distances from (x, y) to (4, 0) and from (x, y) to (-4, 0) is 10.       Log On


   

Question 945704: Find a formula for the set of all points (x, y) for which the sum of the distances from (x, y) to (4, 0) and from (x, y) to (-4, 0) is 10.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You may be describing an ellipse. Use the Distance Formula with your description. The foci are (4,0) and (-4,0), and the needed sum of distances, 10.

sqrt%28%28x-4%29%5E2%2B%28y-0%29%5E2%29%2Bsqrt%28%28x-%28-4%29%29%5E2%2B%28y-0%29%5E2%29=10

Simplify that, and put into whatever form you need. The center will be (0,0).

sqrt%28%28x-4%29%5E2%2By%5E2%29%2Bsqrt%28%28x%2B4%29%5E2%2By%5E2%29=10

sqrt%28%28x-4%29%5E2%2By%5E2%29=10-sqrt%28%28x%2B4%29%5E2%2By%5E2%29

%28x-4%29%5E2%2By%5E2=100-20sqrt%28%28x%2B4%29%5E2%2By%5E2%29%2B%28x%2B4%29%5E2%2By%5E2

%28x-4%29%5E2=100-20sqrt%28%28x%2B4%29%5E2%2By%5E2%29%2B%28x%2B4%29%5E2

%28x-4%29%5E2-%28x%2B4%29%5E2-100=-20%2Asqrt%28%28x%2B4%29%5E2%2By%5E2%29

x%5E2-8x%2B16-%28x%5E2%2B8x%2B16%29-100=-20sqrt%28%28x%2B4%29%5E2%2By%5E2%29

-16x-100=-20sqrt%28%28x%2B4%29%5E2%2By%5E2%29

4x%2B25=5sqrt%28%28x%2B4%29%5E2%2By%5E2%29
Not finished. Square both sides and continue simplifying.