analytic geometry helps are appreciated

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For some positive real number r , the line x+y=r is tangent to the circle x^2+y^2 = r. Find r.

How do we do this? Set equal equations together??

  • analytic geometry helps are appreciated -

    r^1/2 is the radius of the circle.
    r is the y-intercept of the line
    y = r - x.
    It is tangent to the circle if
    r^2 = 2*(sqrtr)^2
    (from Pythagorean rule)
    Therefore r^2 = 2r
    r = 2

    Plot the two functions
    y = 2-x and
    x^2 + y^2 = 2
    You will see that there is tangency at
    (sqrt2, sqrt2)

  • analytic geometry helps are appreciated -

    thanks a bunch sire

  • analytic geometry helps are appreciated -

    Yes set the two equations equal to each other. You then get that r = 2. I'm not going to tell you all of the work because drwls has already answered.

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