# Find an equation of the parabola with focus (2, 1) and directrix x = -4?

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- jacob sLv 75 months ago
Considering the general equation of the parabola (y-k)^2 = 4p(x-h)....Where (h,k) is the vertex: p is the distance from the vertex to the directrix and also the distance from the vertex to the focus.

focus (2,1), directrix x = -4

((2 +(-4))/2, 1)= (-1,1)

(y-k)^2 = 4p(x-h)

(y-1)^2 = 4p(x-(-1))

(y-1)^2 = 4p(x+1)

p=√[(2-(-1))^2 +(1-1)^2]

p=√3^2

p= 3

(y-1)^2 = 4(3)(x+1)

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