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September 30th, 2012, 03:22 PM  #1 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  finding a point on a circle given the slope of the tan line
x^(2) + y^(2) = 100 mT = 3/4 Can someone show me how to go about finding this? 
September 30th, 2012, 03:48 PM  #2 
Senior Member Joined: Jul 2011 Posts: 118 Thanks: 0  Re: finding a point on a circle given the slope of the tan l
You can transform circle equation into function for upper and lower semicircle: and now take derivative 
September 30th, 2012, 04:02 PM  #3 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: finding a point on a circle given the slope of the tan l
forgive me but wouldn't I take the Derv to find the slope of the tan line? I am trying to find a point on the upper half of the circle. I have tried to think on my own hence: rise/run and point slope yy1=m(xx1) when I to that I get (3/4, 0) would this be right? 
September 30th, 2012, 04:43 PM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: finding a point on a circle given the slope of the tan l Hello, mathkid! Quote:  
September 30th, 2012, 05:01 PM  #5 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: finding a point on a circle given the slope of the tan l
Wow!

September 30th, 2012, 08:46 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: finding a point on a circle given the slope of the tan l
Another approach: Implicitly differentiate with respect to x: Equate this to Substitute into original equation: Take positive root. 
October 1st, 2012, 06:49 PM  #7 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: finding a point on a circle given the slope of the tan l
You don't have to differentiate at all. Any tangent line to a circle is perpendicular to the radius at that point. If the slope of the tangent line is 3/4, then the radius at that point has slope 4/3. But if (x,y) is a point on the circle, then the slope of the line from the center, the origin (0, 0), is y/x. That is, y/x= 4/3 and, of course, . From y/x= 4/3, y= (4/3)x so or , and then .


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circle, finding, line, point, slope, tan 
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