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Math Help - Analytic Geometry Homework

  1. #1
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    Analytic Geometry Homework

    Well I'm kinda stumped and I need you guys...

    1.) The length of a diameter of a circle described by 9x^2 + 9y^2 = 16 is?

    2.) Find the equation of the circle with center on x+y = 4 and 5x+2y+1=0 and having a radius of 3.
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  2. #2
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    Quote Originally Posted by valcross View Post
    Well I'm kinda stumped and I need you guys...

    1.) The length of a diameter of a circle described by 9x^2 + 9y^2 = 16 is?

    1)

    9x^2 + 9y^2 = 16
    x^2 + y^2 = \frac{16}{9}
    As general form is x^2 + y^2 = r^2
    \implies r^2 = \frac{16}{9}
    r = \frac{4}{3}
    Diameter is two times radius.
    \therefore d=\frac{8}{3}
    Last edited by Simplicity; March 4th 2008 at 10:39 AM. Reason: Question Clarification
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  3. #3
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    Regarding #2:

    The equation for a circle with center (h,k) and radius r is:

    (x-h)^2 + (y-k)^2 = r^2.

    So you know r = 3. Where's the center?

    Recall that it lies on the two lines given, so find the intersection of the two lines. I did it by substitution, starting with the first equation, which gives:

    y=4-x.

    Sub this into the other equation for y, which gives:

    5x+8-2x+1=0

    3x+9=0

    3x=-9

    x=-3.

    Recall y=4-x, so y=4-(-3)=7.

    So your center is at (-3,7). Now you know h, k, and r, the three essentials for writing the equation of a circle.

    There you are!
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  4. #4
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    Thanks guys, that was very educational, not to mention I now have my homework done thanks to you.
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