SOLUTION: I can not figure out how to write an equation for parabola focus (3,8),directrix y=4

Question 81488This question is from textbook Algebra 2
: I can not figure out how to write an equation for parabola
focus (3,8),directrix y=4 This question is from textbook Algebra 2

Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
write an equation for parabola
focus (3,8),directrix y=4
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Draw the line y=4.
Plot the point (3,8)
The focus is above the directrix and is 2p away from it.
So 2p=4; p=2
The vertex is half way between the focus and the directrix.
So the vertex is (3,6)
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EQUATION:
4p(y-k)=(x-h)^2
8(y-6)=(x-3)^2
8y-48=x^2-6x+9
8y=x^2-6x+57
y=(1/8)x^2-(3/4)x+57/8
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Cheers,
Stan H.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a parabola is made up of points that are equidistant from a given point (focus) and a given line (directrix)

the "distance formula" gives the distance between (x,y) and (3,8) as

the distance between (x,y) and y=4 is y-4 ... x is not involved

setting these equal gives ... squaring both sides gives

... ...

so ........THIS ANSWER HAS BEEN CORRECTED (with my apologies)