Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. At positions where f does not evaluate to a real number, holes are left so that the background to the contour plot shows through. Or perhaps I don’t understand why you are concerned about the output. The focus and conic section directrix were considered by Pappus MacTutor Archive. Post as a guest Name. Enable JavaScript to interact with content and submit forms on Wolfram websites. ContourPlot has attribute HoldAll , and evaluates the f i and g i only after assigning specific numerical values to x and y. Letting be the ratio and the distance from the center at which the directrix lies, then.

ContourPlot initially evaluates f at a grid of equally spaced sample points specified by PlotPoints. Sign up using Facebook. How many pixels have you given it in which to draw those points in the x-direction? This isn’t the only function which gives bad output – its actually quite common. So you would see an “empty” plot, which is even more non intuitive Hints help you try the next step on your own. This produces a torus.

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### Circle, Ellipse, Hyperbola, and Astroid – Wolfram Demonstrations Project

The focus and conic section directrix were considered by Pappus MacTutor Archive. Enable JavaScript to interact with content and submit forms on Wolfram websites.

At first I though that the X plane IS 0 – so it was very weird that the graph passed it.

The error says it’s incorrect syntax, although I can’t see any errors. Which should llot the points it generated the lines between, gives me this: The arc lengthcurvatureand tangential angle for the above parametrization are.

Parametric equations for the right branch of a hyperbola are given by.

I think that what you are seeing is an artefact common to most computer-based drawings: A theorem of Apollonius states that for a line segment tangent to the hyperbola at a point and intersecting the asymptotes at points andthen is constant, and right figure above; Wells Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and mathemaica. Varying t produces circular motion in the – plane, and linear motion in the direction.

By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. The hyperbola has the important property that a ray originating at a focus reflects in such a way mqthematica the outgoing path lies along the line from the other focus through the point of intersection right figure above.

### plotting – How can I plot a hyperbola from its complex representation? – Mathematica Stack Exchange

How many pixels have you hyperhola it in which to draw those points in the x-direction? Letting fall on the left -intercept requires that. Hyperbola ContourPlot missing input Ask Question.

Varying u yields a circle, while varying t rotates the circle around the axis to form the torus.

The locus of the apex of a variable cone containing an ellipse fixed in three-space is a hyperbola through the foci of the ellipse. Sign up using Email and Password. You should be careful, for example, to avoid parametrizations in which all or part of your surface is covered more than once. Hilbert and Cohn-Vossenp. Contact the MathWorld Team. The X axis is actually 0.

Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. Home Questions Tags Users Unanswered. Enable JavaScript to interact with content and submit forms on Wolfram websites.

## Parametric Plots

You should realize that since it uses only a finite number of sample points, it is possible for ContourPlot to miss features of your functions. The Double Cone Phil Ramsden.

The hyperbola was given its present name by Apollonius, who was the first to study both branches. In a parametric plot, you give both the and coordinates of each point as a function of a third parameter, say.

The arguments supplied to functions in MeshFunctions and RegionFunction are xyyyperbola. Sign up using Email and Password. In polar coordinatesthe equation of a hyperbola centered at the origin i. Then it uses an adaptive algorithm to subdivide at most MaxRecursion times to generate smooth contours. Sign up or log in Sign up using Google.