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Math Help - Circle - System of inequalities

  1. #1
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    Circle - System of inequalities

    A ring on an archery target is bounded by two circles of radii 2ft and 3ft, respectively. Suppose the origin is at the center of the target. Write a system of inequality whose solution is the ring.

    Where do I start?

    I know that an equation for a circle is (x-h)^2 + (y-k)^2 = r^2

    So would the inequality be x^2 + y^2 < 4 and x^2 + y^2 < 9 ?
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  2. #2
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    Hello, chrozer!

    A ring on an archery target is bounded by two circles of radii 2ft and 3ft.
    Suppose the origin is at the center of the target.
    Write a system of inequality whose solution is the ring.
    You were quite close . . .


    The ring is the area outside of the smaller circle, x^2+y^2 \:=\:4
    . . and inside the larger circle, x^2+y^2 \:=\:9


    So we want: . \begin{Bmatrix}x^2+y^2 & > & 4 \\ x^2+y^2 & < & 9 \end{Bmatrix}


    If the circles themselves are included as part of the ring,
    . . then we'll use \geq and \leq.

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, chrozer!

    You were quite close . . .


    The ring is the area outside of the smaller circle, x^2+y^2 \:=\:4
    . . and inside the larger circle, x^2+y^2 \:=\:9


    So we want: . \begin{Bmatrix}x^2+y^2 & > & 4 \\ x^2+y^2 & < & 9 \end{Bmatrix}


    If the circles themselves are included as part of the ring,
    . . then we'll use \geq and \leq.

    Ok. I see....thanx alot.
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