This question is about how to use MMA to plot a curve from solution of a group of parametric equations. To take an algebraic equations as an example, like:

\begin{align} x^2 - y^2 &= t^2 \\ xy &= t \qquad , \end{align} where the range of the parameter $t$: $t \leq - \frac{1}{\sqrt{2}}$ and $t \geq \frac{1} {\sqrt{2}}$.

I managed to solve the equations to get an explicit form via MMA:

 Solve[{-x^2 + y^2 == t^2, x y == t}, {x, y}]

but I don't know how to plot the graph $\{x,y\}$ under the range $t \leq - \frac{1}{\sqrt{2}}$ and $t \geq \frac{1} {\sqrt{2}}$.

Based on rhermans's code, I plotted two graphics for $t≤−1/\sqrt{2}$ and $t≥ 1/\sqrt{2}$, respectively, and used show to combine the two results into one single graph.

The problem is solved.

  • $\begingroup$ That is actually referred to as an implicit form. If you look for "plot implicit function" (without the quotes) in the help browser, first hit is to ContourPlot. $\endgroup$ – Daniel Lichtblau May 29 '18 at 19:08
  {x, y} /. Solve[{-x^2 + y^2 == t^2, x y == t}, {x, y}]
 , {t, -(1/Sqrt[2]), 1/Sqrt[2]}
 , PlotTheme -> "Scientific"
 , AspectRatio -> 1

Mathematica graphics

| improve this answer | |
  • $\begingroup$ Hey, @rhermans, Thank you! I put your code in MMA and just replace {t, -(1/Sqrt[2]), 1/Sqrt[2]} with {t, -8, -1/Sqrt[2]} to plot one part of the range($ t \leq -1/\sqrt{2}$), or with {t, 1/Sqrt[2],8} to plot the other part ($t \geq 1/\sqrt{2}$). Is there any smarter way to plot the two parts in a single graph? $\endgroup$ – Zoe Rowa May 29 '18 at 15:47
  • 1
    $\begingroup$ @ZoeRowa Read this first. You should ask a new question and explain clearly what you need now. $\endgroup$ – rhermans May 29 '18 at 15:50

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