       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.
>
>
>Tom Moriarty
>
>
>
>

```

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