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Math Help - Equation of a half circle

  1. #1
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    Equation of a half circle

    Find an expression for the for the function whose graph is the given curve. Give the domain and range.

    The bottom half of the circle whose center is @(3,0) and has a radius of length 5.



    I'm so lost.
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  2. #2
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    Here is the equation of the whole circle.

    (x-3)^2+y^2=5^2

    Now find y1 and y2, the negative square root would be the botom half of the circle.

    Regards.
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  3. #3
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    Lets find the equation of the full circle first.


    This is y^2 + (x-3)^2 = 5^2


    Rearrange for Y

    This is y = \sqrt{25 - (x-3)^2}

    When it is in this form, the range and domain are defined as follows:
    The domain is all possible values that x can take
    The range is all possible values that y can take


    Because it is a circle with radius 5, centered around (3,0); you know the domain and range are:
    Domain:   -2 \leq x \leq 8
    Range:   -5 \leq y \leq 5



    You want the bottom half of the circle, which is the part where Y<0.
    Hopefully, you can see that
    Domain:   -2 \leq x \leq 8 (the same)
    Range:   -5 \leq y \leq 0 (bottom half only)


    This is much easier to draw than do in your head. I'll try to attach an image later



    edit too slow
    Attached Thumbnails Attached Thumbnails Equation of a half circle-circles.jpg  
    Last edited by SpringFan25; June 7th 2010 at 12:44 PM.
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  4. #4
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    I got the same answer as SpringFan25.
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