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Math Help - L is Tangent to C?

  1. #1
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    L is Tangent to C?

    Hey,

    I must be an idiot because the answer to this is probably simple.

    Anywho.

    Circle has equation X^2+y^2+4x-8y+10=0

    So Center is (-2,4) and Radius is Route 10.

    Now L has an equation X-3y+4=0

    All I have to do is show that L is a tangent to C.
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  2. #2
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    Quote Originally Posted by StephenPoco View Post
    Hey,

    I must be an idiot because the answer to this is probably simple.

    Anywho.

    Circle has equation X^2+y^2+4x-8y+10=0

    So Center is (-2,4) and Radius is Route 10.

    Now L has an equation X-3y+4=0

    All I have to do is show that L is a tangent to C.
    If L is a tangent to C then they must have a common point, say (x_0,y_0).

    Common point means:
    x_0^2+y_0^2+4x_0-8y_0+10=0, \, x_0-3y_0+4=0

    Now solve these two equations simultaneously. Then (x_0,y_0) will satisfy both and be the required common point.
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