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 March 7th, 2010, 10:23 AM #1 Newbie   Joined: Mar 2010 Posts: 2 Thanks: 0 Finding equation of a circle without knowing its radius Find the equation of the circle centered at (3,0) that intersects the curve y=x^2 at exactly one point.
 March 7th, 2010, 11:52 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,948 Thanks: 1139 Math Focus: Elementary mathematics and beyond Re: Finding equation of a circle without knowing its radius (x - 3)^2 + y^2 = r^2 x^2 - 6x + 9 + y^2 = r^2 2x - 6 + 2yy' = 0 y' = (6 - 2x)/(2y) and, from the other equation, y' = 2x. 2x = (6 - 2x)/(2y) 2x = (6 - 2x)/(2x^2) [sub in x^2 for y.] 2x - 6 + 4x^3 = 0, x = 1 so r^2 = 5.

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