My Math Forum Equation of a drawn line tangent to elliptic curve

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December 10th, 2012, 08:00 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, 09:30 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 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: $y=4x+9$ $y=-\frac{1}{4}x+\frac{5}{2}$

 Tags curve, drawn, elliptic, equation, line, tangent

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