What is the equation of the parabola with a focus at (5,23) and a directrix of y= 17?

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Answer 1 · 2016-02-06T14:54:32

#y=1/12(x^2-10x+265)#

Distance from focus to the directrix#=6#. Therefore, #p=3#
Vertex is at #(5, 20)#

use the form #(x-h)^2=4p(y-k)#

#(x-5)^2=4(3)(y-20)#

#x^2-10x+25=12y-240#

#x^2-10x+265=12y#

#y=1/12(x^2-10x+265)#

graph{(y-(x^2-10x+265)/12)(y-17)=0[-45,45,-5,45]}

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