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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: 7,923 Thanks: 1123 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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circle, equation, finding, knowing, radius 
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