SOLUTION: We did not find results for: determine the equation of the ellipse such that the sum of the distances of any point of curve from 2 points whose coordinates are (-3,0) and (3,0) is

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: We did not find results for: determine the equation of the ellipse such that the sum of the distances of any point of curve from 2 points whose coordinates are (-3,0) and (3,0) is       Log On


   

Question 1003727: We did not find results for: determine the equation of the ellipse such that the sum of the distances of any point of curve from 2 points whose coordinates are (-3,0) and (3,0) is always equal to 8
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You have the definition, so just use the Distance Formula and simplify into the standard form equation for the ellipse. This means, DERIVE the equation starting with the use of Distance Formula.

The points on the ellipse are some set of unknown points, (x,y).

Initial Set-up, sqrt%28%28x-%28-3%29%29%5E2%2B%28y-0%29%5E2%29%2Bsqrt%28%28x-3%29%5E2%2B%28y-0%29%5E2%29=8

Beginning steps,
sqrt%28%28x%2B3%29%5E2%2B%28y%29%5E2%29%2Bsqrt%28%28x-3%29%5E2%2B%28y%29%5E2%29=8

sqrt%28%28x%2B3%29%5E2%2By%5E2%29%2Bsqrt%28%28x-3%29%5E2%2By%5E2%29=8

sqrt%28%28x%2B3%29%5E2%2By%5E2%29=8-sqrt%28%28x-3%29%5E2%2By%5E2%29

First Squaring of both sides,
%28x%2B3%29%5E2%2By%5E2=8%5E2-16sqrt%28%28x-3%29%5E2%2By%5E2%29%2B%28x-3%29%5E2%2By%5E2
...
...
...and thirteen more steps done on paper which will be difficult to type-in all the text of them here; lead to highlight%28x%5E2%2F16%2By%5E2%2F7=1%29.