Math

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Find the vertex, focus and directrix of the parabola.

4x - y^2 - 2y - 33 = 0

y^2+2y+1 = -4x+33+1
(y+1)^2 = -4(x+8.5)

vertex:(-1,-8.5)
focus:(-2,-8.5)
Directrix: x=0

Is this correct?

  • Math -

    y^2 + 2 y = 4 x - 33

    y^2 + 2 y + 1 = 4 x - 32

    (y+1)^2 = 4 (x-8)
    (8,-1) is the vertex etc.
    opens right, a = 4
    vertex to focus = 4 so focus at (12,-1)
    vertex to directrix = 4 so directrix at x = 4

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