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Math Help - Circle problem

  1. #1
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    Circle problem

    find a formula for the following function

    the top half of a circle with center (a,b) and radius r

    need some help with this one thanks...
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  2. #2
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    Every point (x,y) on the graph of a circle of radius r satisfies the following relationship:

    x^2+y^2 = r^2

    So to express y as a function of x rewrite:

    y = \pm \sqrt{r^2-x^2}

    The top half of the circle is just y = \sqrt{r^2-x^2}

    Now to shift this function to be centered at (a,b) we have to shift the function up by b and over by a.

    y = \sqrt{r^2-(x-a)^2}+b
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by mathlete View Post
    find a formula for the following function

    the top half of a circle with center (a,b) and radius r

    need some help with this one thanks...
    The equation of a circle with center (a,b) is given by
    (x-a)^2+(y-b)^2=r^2

    to find the top half we need to isolate y and take the positive square root

    (y-b)^2=r^2-(x-a)^2 taking the postive root

    y-b=\sqrt{r^2-(x-a)^2 }

    so we get...

    y=b+\sqrt{r^2-(x-a)^2 }
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  4. #4
    Senior Member topher0805's Avatar
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    The equation of a circle is:

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

    Where (h,k) is the center of the circle.

    The equation for the two halves of a circle are given by isolating y.

    y = \pm \sqrt {r^2 - (x-h)^2} + k

    We are only interested in the top half so we only take the positive square root:

    y = \sqrt {r^2 - (x-h)^2} + k
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