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Homework Help: Finding the equation of the circle given two points and a tangent line

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the equation of the circle that passes through the point (3,-2) and tangent to the line y=3x+5 at (-1,2). Answer in standard form.

    2. Relevant equations
    d= |mx0+b-y0|

    is needed to find the radius of the circle
    (x-h)2+(y-k)2=r2 is needed to find the equation of the circle.

    3. The attempt at a solution

    I haven't attempted a solution per se, but I do know that I need to find the center of the circle. However I don't see a way to find the center of a circle.
  2. jcsd
  3. Feb 9, 2010 #2


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    Gold Member

    You need to figure out h, k, and r, right? Three unknowns. Here are a couple of suggestions, depending on whether you know any calculus.

    If you know calculus, you can get three equations in the three unknowns by using the fact that your two given points must work in the equation, and the slope of the circle must equal the slope of the tangent line where they touch.

    If you can't use calculus, write the equation of the line perpendicular to the tangent line at (-1,2) and find the point on that line that is equidistant from your two given points. That will be your center.
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