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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 y-y1=m(x-x1) when I to that I get (3/4, 0) would this be right? September 30th, 2012, 04:43 PM   #4
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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: 521 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 . Tags circle, finding, line, point, slope, tan ,

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### find the point when the equation of tangent and slope are given

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