SOLUTION: Write an Equation given focus (1, -3) directrix y= -5

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Question 1010584: Write an Equation given focus (1, -3) directrix y= -5
Answer by MathLover1(20850) About Me  (Show Source):
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Write an Equation
given focus (1, -3)
directrix y=+-5
One way is try the definition of a parabola and the use of the Distance Formula.
Cutting past all the instructive description, the directrix is all points, (x,-5). The parabola is a variable set of points, (x,y):
so, we use points (1, -3) and (x,-5)


sqrt%28%28x-1%29%5E2%2B%28y%2B3%29%5E2%29=sqrt%28%28x-x%29%5E2%2B%28y%2B5%29%5E2%29
%28x-1%29%5E2%2B%28y%2B3%29%5E2=%280%29%5E2%2B%28y%2B5%29%5E2
x%5E2-2x%2B1%2By%5E2%2B6y%2B9=y%5E2%2B10y%2B25
x%5E2-2x%2B1%2B9-25=10y-6y
x%5E2-2x-15=4y
y=%281%2F4%29x%5E2-%281%2F2%29x-15%2F4
or
y+=+%281%2F4+%29%28x%5E2-2x-15%29