SOLUTION: Find the equation of the parabola with focus F(4,0) and directrix x=3 by using the Distance formula

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Question 870622: Find the equation of the parabola with focus F(4,0) and directrix x=3 by using the Distance formula
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The distance between F and any (x,y) is equal to the distance between the directrix (3,y) and (x,y).

sqrt%28%28x-4%29%5E2%2B%28y-0%29%5E2%29=sqrt%28%28x-3%29%5E2%2B%28y-y%29%5E2%29

sqrt%28%28x-4%29%5E2%2By%5E2%29=sqrt%28%28x-3%29%5E2%29
%28x-4%29%5E2%2By%5E2=%28x-3%29%5E2
x%5E2-8x%2B16%2By%5E2=x%5E2-6x%2B9
-8x%2B16%2By%5E2=-6x%2B9
-2x%2B16%2By%5E2=9
-2x=-y%5E2%2B9-16
2x=y%5E2%2B16-9
2x=y%5E2%2B7
highlight%28x=%281%2F2%29y%5E2%2B7%2F2%29