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Math Help - Equation of a parabola Given Focus and Directrix

  1. #1
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    Equation of a parabola Given Focus and Directrix

    Need some help writting a formula for this conic section.

    Given: Focus is (1,1) and directrix is y=-x-2

    Thanks
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  2. #2
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    You can use the distance formula and the formula for the distance from a point to a line.

    \sqrt{(x-1)^{2}+(x-1)^{2}}=\frac{|x+y+2|}{\sqrt{2}}

    Square both sides:

    2(x-1)^{2}=\left(\frac{x+y+2}{\sqrt{2}}\right)^{2}

    Expand and simplify.
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  3. #3
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    Quote Originally Posted by galactus View Post
    You can use the distance formula and the formula for the distance from a point to a line.

    \sqrt{(x-1)^{2}+(x-1)^{2}}=\frac{|x+y+2|}{\sqrt{2}}

    Square both sides:

    2(x-1)^{2}=\left(\frac{x+y+2}{\sqrt{2}}\right)^{2}

    Expand and simplify.
    thanks. Anyone else?
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  4. #4
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    Quote Originally Posted by Daddycakes View Post
    thanks. Anyone else?
    Anyone else for what? Show us what you have done after galactus' post. If you can't get any further than that point, let us know. Be specific!

    -Dan

    Edit: Actually a slight change is needed here:
    \sqrt{(x-1)^{2}+(x-1)^{2}}=\frac{|x+y+2|}{\sqrt{2}}

    should be
    \sqrt{(x-1)^{2}+(y-1)^{2}}=\frac{|x+y+2|}{\sqrt{2}}

    So
    (x - 1)^2 + (y - 1)^2 = \frac{(x + y + 2)^2}{2}

    -Dan
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