SOLUTION: Find the equation of the parabola whose focus is (-1,2)and directrix is x-2y-15=0.

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Question 878549: Find the equation of the parabola whose focus is (-1,2)and directrix is x-2y-15=0.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The set of points (x,y) must be equally distant from (-1,2) and from x=2y%2B15. The general variable ordered pair for the directrix is (2y+15,y).

Going one step past the radical form of the distance formula expressions,
%28x-%28-1%29%29%5E2%2B%28y-2%29%5E2=%28x-2y-15%29%5E2%2B%28y-y%29%5E2
%28x%2B1%29%5E2%2B%28y-2%29%5E2=%28x-2y-15%29%5E2
x%5E2%2B2x%2B1%2By%5E2-4y%2B4=x%5E2-4xy-30x%2B60y%2B225
2x%2B1%2By%5E2-4y%2B4=-4xy-30x%2B60y%2B225
2x%2B1%2By%5E2-4y%2B4%2B4xy%2B30x-60y-225=0
32x-220%2By%5E2-4y%2B4xy-60y=0
y%5E2%2B4xy-4y-60y%2B32x-220=0
y%5E2%2B4xy-64y%2B32x-220=0
highlight%28y%5E2-64y%2B4xy%2B32x-220=0%29