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Math Help - Circle Geometry

  1. #1
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    Exclamation Circle Geometry

    Circle Diagram - http://i39.tinypic.com/33z48yq.png

    1. The diagram shows a circle with centre (2,1) and radius 5.

    a) Show that the equation of the circle may be written as:

    x^2 + y^2 - 4x - 2y - 20 = 0

    b) Find the coordinates of the Points P and Q where the circle cuts the y-axis. Leave your answers in the form a(+ or -) sqrt [b].

    c) Verify the point A (5,-3) lies on the circle.

    Show that the tangent to the circle at A has equation 4y = 3x - 27.

    Thanks!
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  2. #2
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    Okay, I have worked out part a) by completing the square. (x - 2)^2 + (y - 1)^2 = 25

    I still can't understand part b) or c) though.
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  3. #3
    MHF Contributor
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    Hi

    b) The y-axis equation is x=0
    The circle cuts the y-axis for the coordinates satisfying both
    x=0 and x + y - 4x - 2y - 20 = 0
    thus x=0 and y-2y-20=0

    c) You just need to show that both x=5 and y=-3 satisfy the equation x + y - 4x - 2y - 20 = 0

    The tangent to the circle at A is perpendicular to \overrightarrow{CA} and passes through A
    Last edited by running-gag; February 8th 2009 at 11:25 AM.
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