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Math Help - tangent question

  1. #1
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    tangent question

    The circle  (x+3)^2+(y-4)^2=r^2 is a tangent to the parabola y=(x+3)^2+6
    Find the coordinates where the circle is tangent to the parabola.
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  2. #2
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    Hello, requal!

    A strange problem . . .


    The circle  (x+3)^2+(y-4)^2\:=\:r^2 is a tangent to the parabola y\:=\:(x+3)^2+6
    Find the coordinates where the circle is tangent to the parabola.
    Make a sketch!

    The parabola opens upward with vertex (-3,6).
    The circle has center (-3,4) and radius r.

    Since the center of the circle is directly below the vertex of the parabola,
    . . the only point at which they can be tangent is at the vertex: . \begin{array}{c}\cup \\ ^{\bigcirc}\end{array}\!\!\!\leftarrow

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