What is the vertex form of the equation of the parabola with a focus at #(21,35)# and a directrix of #y=25 #?

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Answer 1 · 2017-11-07T23:12:44

#y = 1/(20)(x-21)^2 + 30#

The vertex form of the equation of a parabola with a horizontal directrix is:

#y = 1/(4f)(x-h)^2 + k" [1]"#

where #h = x_"focus"#, #k = (y_"focus" + y_"directrix")/2#, and #f = y_"focus" - k#

In our case,

#h = 21#

#k = (35+25)/2#

#k = 30#

#f = 35 - 30#

#f = 5#

Substitute these values into equation [1]:

#y = 1/(20)(x-21)^2 + 30" [2]"#