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Math Help - Sorry asking for so much help

  1. #1
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    Sorry asking for so much help

    I have more questions, sorry to bother

    they ask me to write the equation in standard form, then find the center and radius x^2+y^2+8x+7= 0

    they also ask me to find the vertex, focus and the lenght of the lactus rectum 8y=x^2

    and just one last, so sorry to ask for that much help

    find the equation of the parabola that has a focus at (-3,4) and directriz y=2

    thank you.
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  2. #2
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    first problem first

    Quote Originally Posted by jhonwashington View Post
    I have more questions, sorry to bother

    they ask me to write the equation in standard form, then find the center and radius x^2+y^2+8x+7= 0

    ...
    Hello,

    you have: x^2+y^2+8x+7= 0 . Now accomplish the squares:
    x^2+8x+16+y^2=-7+16
    (x+4)^2+y^2=9. This equation describes a circle with the centre M(-4, 0) and the radius r = 3.

    EB
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  3. #3
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    Quote Originally Posted by jhonwashington View Post
    ...

    they also ask me to find the vertex, focus and the lenght of the lactus rectum 8y=x^2...
    Hello,

    the general form of your parabola is: x^2 = 2p \cdot y. This is a parabola which opens up and has it's vertex at V(0, 0). The focus has the (general) coordinates F\left(0,\frac{p}{2}\right). With your equation it becomes: F\left(0,2\right).
    The lactus rectum is the chord passing through the focus and perpendicular to the (main) axis. With a parabola the lactus rectum has always the length 2p. In your case the lactus rectum is 8.

    EB
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  4. #4
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    Quote Originally Posted by jhonwashington View Post
    I have more questions, ...
    find the equation of the parabola that has a focus at (-3,4) and directriz y=2.
    Hello,

    the directriz is below the focus thus the parabola opens upward and the main axis is x = -3.

    The midpoint on the main axis between the focus and the directriz is the vertex V(d, c) thus your vertex is V(-3, 3).

    The general form of your parabola is:
    (x-d)^2=2p\cdot (y-c)

    The distance between focus and directriz is p.

    Plug in the values you know:

    (x+3)^2=2\cdot 2\cdot (y-3). Solve for y:

    y=\frac{1}{4}x^2+\frac{3}{2}x+\frac{21}{4}

    EB
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  5. #5
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    thanks earboth, I wish I were as smart as you are.
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