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

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  • 5 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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