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Implicit Graphing on TI-Nspire CAS
TNS sampler document
Implicit graphing of relations in two variables is possible with TI-Nspire CAS, using the zeros command. In the Calculator, zeros(x2-y2-4,y) will take an expression in two variables and return as a list, where possible, the symbolic forms of the function with y isolated. Graphs & Geometry can graph such a list of functions, and so we see the implicit plot.
The video shows the syntax and some of the possibilities for this form.
For non-CAS, the same effect is possible using the nSolve command, although the method is much slower, especially on the handheld. For example, to plot the hyperbola, x2 - y2 = 4, define:
f1(x) = nSolve(x2 - y2 = 4,y)
f2(x) = nSolve(x2 - y2 = 4,y=-2)
nSolve takes an equation as its argument, while zeros requires an expression. nSolve will always require multiple applications to achieve a complete curve.
An application of this method uses a simple function called fiveptconic (available from the add2cas library) which takes coordinates of five points and plots the conic which passes through these.
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