SOLUTION: find the general equation of the parabola whose focus is (2,3) and directrix is x-4y+3=0

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Question 1037767: find the general equation of the parabola whose focus is (2,3) and directrix is x-4y+3=0
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The general point for the parabola is (x,y) and the directrix is y=x%2F4-3%2F4.

Distance from general point to either focus or directrix is equal. (Definition of a parabola).

-----Using the Distance Formula.

%28x-2%29%5E2%2B%28y-3%29%5E2=0%5E2%2B%28y-%28x%2F4-3%2F4%29%29%5E2

%28x-2%29%5E2%2B%28y-3%29%5E2=%28y-x%2F4%2B3%2F4%29%5E2



%28x-2%29%5E2%2B%28y-3%29%5E2=y%5E2-xy%2F2%2Bx%5E2%2F16-6x%2F16%2B6y%2F4%2B9%2F16

%28x-2%29%5E2%2B%28y-3%29%5E2=y%5E2-xy%2F2%2Bx%5E2%2F16-3x%2F8%2B3y%2F2%2B9%2F16

Multiply the members by 16 to clear away denominators.
16%28x-2%29%5E2%2B16%28y-3%29%5E2=16y%5E2-8xy%2Bx%5E2-6x%2B24y%2B9

16%28x%5E2-4x%2B4%29%2B16%28y%5E2-6y%2B9%29=16y%5E2-8xy%2Bx%5E2-6x%2B24y%2B9

16x%5E2-64x%2B64%2B16y%5E2-96y%2B144=16y%5E2-8xy%2Bx%5E2-6x%2B24y%2B9

15x%5E2-64x%2B64-96y%2B144=-8xy-6x%2B24y%2B9

15x%5E2-64x%2B6x%2B64-96y-24y%2B8xy-9=0

highlight%2815x%5E2-58x-120y%2B8xy%2B55=0%29