Plot the curve of a group of parametric equations [closed]

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.

closed as off-topic by Daniel Lichtblau, halirutan♦, MarcoB, Henrik Schumacher, SektorMay 30 '18 at 8:40

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Daniel Lichtblau, halirutan, MarcoB, Henrik Schumacher, Sektor
If this question can be reworded to fit the rules in the help center, please edit the question.

• 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. – Daniel Lichtblau May 29 '18 at 19:08

1 Answer

ParametricPlot[
Evaluate[
{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
]


• 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? – Zoe Rowa May 29 '18 at 15:47
• @ZoeRowa Read this first. You should ask a new question and explain clearly what you need now. – rhermans May 29 '18 at 15:50