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2 December, 14:57

Which is the standard form of the equation of a parabola with a focus of (8, 0) and directrix x = - 8?

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  1. 2 December, 16:09
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    With a parabola that faces left or right it is

    (y-k) ²=4p (x-h)

    p is distance from directix to vertex which is also the distance from vertex to focus

    if it opens to the right, then p is positive

    if it opens to the left, then p is negative

    so we know that directix is-8 and focus is (8,0)

    directix is behind the parabola

    so therfor the parabola opens to the right

    distance from x=-8 to (8,0) is 16 units

    16/2=8

    p=8

    vertex is 8 units to right of directix or 8 units to the left of focus

    (8,0) is focus so vertex is (0,0)

    (h, k) is vertex

    (y-k) ²=4p (x-h)

    (y-0) ²=4 (16) (x-0)

    y²=64x
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