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Thread: Parabolas, Circles, Ellipses & Hyperbolas

  1. #1
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    Parabolas, Circles, Ellipses & Hyperbolas

    Hey everyone! I am in precalculus trig right now and it's been about 7 years since my last math course. Can someone please tell me what I did wrong (probably my algebra?) in solving for the focus for this parabola.

    Given equation: x^2 + 4x + 2y +10 = 0

    to change to standard form I got: (x-(-2))^2 = 4(-1)(-1/2y - 3/2)

    Focus (-2, -5/2) but answer was wrong, should have been (-7/2). Can someone show me how to get this?
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  2. #2
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    Re: Parabolas, Circles, Ellipses & Hyperbolas

    Given equation: x^2 + 4x + 2y +10 = 0
    The standard form is $(x - h)^2 = 4p (y - k)$, where the focus is $(h, k + p)$ and the directrix is $y = k - p$.

    $x^2+4x+4 + 2y + 6 = 0$

    $(x+2)^2 + 2(y + 3) = 0$

    $(x+2)^2 = -2(y + 3)$

    $h = -2$, $k = -3$, $4p = -2 \implies p = -\dfrac{1}{2}$

    vertex at $(-2,-3)$, focus at $\left(-2,-\dfrac{7}{2}\right)$
    Thanks from topsquark and romsek
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