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Math Help - analytic geometry (circles)

  1. #1
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    analytic geometry (circles)

    Find the equation of the circle of radius \sqrt{5} tangent to the line 2x+y-3=0 and having its center on the line 2x+3y = 4.
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    Re: analytic geometry (circles)

    Quote Originally Posted by TechnicianEngineer View Post
    Find the equation of the circle of radius \sqrt{5} tangent to the line 2x+y-3=0 and having its center on the line 2x+3y = 4.
    To do this we must find a point (p,q)\in~2x+3y=4 having distance of \sqrt{5} from 2x+y-3=0.
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    Re: analytic geometry (circles)

    how am i supposed to solve the line perpendicular to the tangent line when i have two unknowns (the coordinates at the center and the end of the circle)
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    Re: analytic geometry (circles)

    Quote Originally Posted by TechnicianEngineer View Post
    how am i supposed to solve the line perpendicular to the tangent line when i have two unknowns (the coordinates at the center and the end of the circle)
    You are not supposed to do that.

    You know that 2p+3q=4 because it is on the line.

    The distance formula gives you \frac{|2p+q-3|}{\sqrt{2^2+1^2}}=\sqrt{5}.
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