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How to plot a parabola (conic): y²=4ax

asked 2015-08-05 18:57:59 -0500

mellow_yellow gravatar image

updated 2015-08-05 18:58:34 -0500

I'm learning about conics, specifically parabolas, and I'd like to plot them. I already know how to do plot(x^2)), but what about y²=4ax ? I understand that representation is a relation, not a function, so that probably eliminates plot(f(x)). But, I'm stuck on how I might plot that so-called "general form" of a parabola.


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answered 2015-08-05 21:54:13 -0500

dazedANDconfused gravatar image

updated 2015-08-05 22:00:26 -0500

You could try plotting it as two functions but implicit_plot is the natural choice. The documentation is here. This simple code illustrates how it could be done, given a specific value of a:

x, y = var('x,y')
implicit_plot(y^2==4*a*x, (x,-2,10), (y,-8,8))

Note the double equal signs. You can run the code in any Sage Cell Server, such as here, to check the result. Plotting it as two functions:

A = plot(2*sqrt(a*x), (x, -2, 10))
B = plot(-2*sqrt(a*x), (x, -2, 10))

and with a little complaining Sage plots over values that avoids problems with the domain.

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Asked: 2015-08-05 18:57:59 -0500

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Last updated: Aug 05 '15