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Conic Parabolas in General Form

  1. Apr 21, 2010 #1
    1. The problem statement, all variables and given/known data

    y2 - 8x + 4y + 12 = 0

    I need to find the vertex, focus, axis of symmetry, directrix, direction and p.

    2. Relevant equations


    3. The attempt at a solution

    No attempt as this is the first one I've encountered in general form. I'm not even looking for an answer, but if someone knows where to find a website or tutorial which helps in solving a conic parabola in this form then it would be very helpful.
  2. jcsd
  3. Apr 22, 2010 #2


    Staff: Mentor

    There are a couple of basic forms.
    (y - k)2 = 4p(x - h)

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

    The first form above opens to the left or right, depending on whether p is negative or positive.

    The second form opens down or up, depending on whether p is negative or positive.

    In both, the vertex of the parabola is at (h, k), the focus is inside the parabola, and |p| units from the vertex, located on the axis of symmetry. The directrix is on the outside of the parabola, and |p| units the other way from the vertex.

    For your problem, put the y terms on one side and the x terms on the other, and complete the square in the y terms. It should look like the first form above.
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