Re: Vertical Tangents

*To*: mathgroup at smc.vnet.net*Subject*: [mg25816] Re: [mg25787] Vertical Tangents*From*: "Tom De Vries" <tdevries at shop.westworld.ca>*Date*: Sat, 28 Oct 2000 01:41:08 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello! I would also be interested in the ImplicitPlot "solution" to the question given below. The way I would get these graphs is really messy so I figure someone knows a better way! This is just a "quick fix" answer... To do these kinds of plots, I have used ContourPlot with options set to get what I want. The line below produces the plot. The Block and Display Function "mess" are not needed if you use the DrawingPaper package created by David Park (which is excellent!) Block[{$DisplayFunction = Identity}, graph1 = ContourPlot[x^2 + x*y + y^2 - 7 , {x, -5, 5}, {y, -5, 5}, ContourShading -> False, Contours -> {0}, Frame -> False, Axes -> True, AxesOrigin -> {0, 0}]; graph2 = ContourPlot[y - 2*Sqrt[7/3], {x, -5, 5}, {y, -5, 5}, ContourShading -> False, Contours -> {0}, Frame -> False, Axes -> True, AxesOrigin -> {0, 0}]; graph3 = ContourPlot[ x - 2*Sqrt[7/3], {x, -5, 5}, {y, -5, 5}, ContourShading -> False, Contours -> {0}, Frame -> False, Axes -> True, AxesOrigin -> {0, 0}]; ]; Show[{graph1, graph2, graph3}, DisplayFunction -> $DisplayFunction]; Sincerely, Tom De Vries ---------- >From: Tom Moriarty <tjmor at erols.com> To: mathgroup at smc.vnet.net >To: mathgroup at smc.vnet.net >Subject: [mg25816] [mg25787] Vertical Tangents >Date: Wed, Oct 25, 2000, 12:53 AM > >This group was very helpful on my last question and I hope you will be >willing to once again come to the aid of a teacher trying to illustrate >to calculus students tangents to implicit plots. By the way, I >purchased Mathematica on my own, it is not available to me at school - >so I plot at home and Xerox handouts for the kids. I have been able to >show them various implicit plots and tangents to them - for example >ImplicitPlot[{x^2 + x*y + y^2==7, y == 2*Sqrt[7/3]},{x,-5,5}] which >clearly shows the ellipse and one of the horizontal tangents (as asked >for in the textbook problem). But the problem also asked for the >vertical tangents, one of which would be x == 2*Sqrt[7/3], but I get the >message that this equation does not have a single variable other than >x. Is there any way to plot a vertical line? > >Let me tell you Mathematica certainly has helped my students (and me) >visualize these implicit plots, without which they are just a matter of >faith. > >Any help you can give me will be greatly appreciated. > >Tom Moriarty > > > >