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December 10th, 2012, 08:00 AM  #1 
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  Equation of a drawn line tangent to elliptic curve
How do you find the equation of a tangent line if you are not given at least the value of one of the coordinates of the intersection? More specifically, this question [attachment=0:zt7jwzk9]Capture.PNG[/attachment:zt7jwzk9] says find the slope of the shown tangent lines to the curve. But there is no indication if the lines are special lines (e.g., a max or a min). From the graph, I can estimate that the lines seem to occur at x=1 and x=2, but cannot really be sure, and the question does not state so. Am I missing something? Thanks 
December 12th, 2012, 09:30 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 462 Math Focus: Calculus/ODEs  Re: Equation of a drawn line tangent to elliptic curve
I would use the (apparent) orthogonality of certain pairs of the tangent lines. In doing so, I get the pair: 

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