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December 10th, 2012, 09:00 AM   #1
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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?

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December 12th, 2012, 10:30 AM   #2
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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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