 illustrates graphs and information of conic sections - Maple Programming Help

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Student[Precalculus][ConicsTutor] - illustrates graphs and information of conic sections

 Calling Sequence ConicsTutor() ConicsTutor(f)

Parameters

 f - (optional) input equation of the conic section in cartesian xy-coordinates or polar rt-coordinates

Description

 • The ConicsTutor command launches a tutor interface that illustrates the graph and provides information about the related conic section.
 • The equation f can be one of the following forms:
 – $\mathrm{expr1}=\mathrm{expr2}$ where $\mathrm{expr1}$ and $\mathrm{expr2}$ are of degree at most 2, in terms of x and y.
 – $\mathrm{expr}$ where $\mathrm{expr}$ is of degree at most $2$ in terms of x and y.
 – $r=g\left(t\right)$ where $g\left(t\right)$ is the polar form of an equation for a conic section, in terms of the variable t.
 – $g\left(t\right)$ where $g\left(t\right)$ is the polar form of an equation for a conic section, in terms of the variable t.
 Note that $g\left(t\right)$ can either be a constant or be in the form $\frac{a}{b+cd\left(t\right)}$ , where a, b, and c are real numbers, and d is the sine or cosine function.
 • If f is not specified, ConicsTutor uses a default function.
 • By default, the tutor returns the plot when you close it.  You can instead choose to return nothing, an embedded table (including the plot and summary information), the command used to generate the plot, or summary information.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Precalculus}\right]\right):$

If the ConicsTutor command is run with no arguments, the default expression is ${x}^{2}+{y}^{2}=1$.

 > $\mathrm{ConicsTutor}\left(\right)$

Circle:

 > $\mathrm{ConicsTutor}\left({x}^{2}+{y}^{2}=1\right)$ Parabola:

 > $\mathrm{ConicsTutor}\left({x}^{2}+2xy+{y}^{2}+2x-2y+4\right)$ Parabola in polar coordinates:

 > $\mathrm{ConicsTutor}\left(r=\frac{1}{1+\mathrm{cos}\left(t+\frac{\mathrm{\pi }}{3}\right)}\right)$ Ellipse:

 > $\mathrm{ConicsTutor}\left({x}^{2}+xy+{y}^{2}-3x-1=0\right)$ Hyperbola:

 > $\mathrm{ConicsTutor}\left(8{x}^{2}+24xy+{y}^{2}+x+2y+1\right)$ 