# Find an equation of the parabola with focus (2,4) and directrix y= -2.

2
by AMDY

2014-05-12T19:04:01+08:00

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Center at (2,1)

(x-2)^2 = 12(y-1)
2014-05-13T09:28:15+08:00

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Center at (2,1) because it is the midpoint of the focus (2,4) and the the point passing by directrix (2,-2).
the latus rectum is equal to 12 because p=3 which is the distance from the center to the focus and the formula of getting latus rectum is 4p then p=3 so therefore latus rectum is equal to 12
the equation of the parabola opens upward so it is " (x-2)^2=12(y-1) "