Find the vertex, focus, directrix, and focal width of the parabola. x= 4y^2?

1 Answer

  • given the horizontal 4p(x − h) = (y − k)^2

    the vertex is at (h,k)

    the focus is at (h+p,k)

    the directrix is at x= h−p

    and the focal width = |4p|

    so x = 4y^2

    ∴ (1/4)(x − 0) = (y − 0)^2

    ∴ 4(1/16)(x − 0) = (y − 0)^2

    so the vertex is at (h,k) = (0,0)

    the focus is at (h+p,k) = (1/16,0)

    the directrix is x = h−p ⇒ x = -1/16

    the focal width is |4p| = 1/4

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