Hyperbola
- Tags
- math
Refers to two curves that are infinite and mirror reflections of each other. These generally have the form \( xy = a^2 \) or in parametric form \( (at, \frac{1}{t}) \).
\begin{figure}
\centering
\begin{tikzpicture}
\begin{axis}[axis lines=middle,samples=400, ymin=-10, ymax=10]
\draw[very thin, gray!30, step=1 cm](-3,-2.9) grid (2.9,2.9);
\addplot[blue,domain=-3:3] {1/x};
\draw[red!20, dashed, line width=0.5mm] (axis cs:0,-10) -- (axis cs:0,10);
\draw[red!20, dashed, line width=0.5mm] (axis cs:-10,0) -- (axis cs:10,0);
\node at (1, 2)[circle,fill,inner sep=1.5pt]{x};
\filldraw[black] (1,2) circle (2pt) node[anchor=west] {Intersection point};
\end{axis}
\end{tikzpicture}
\caption{Demonstration of a hyperbola.}
\end{figure}Constant Area Property
The area between the \(x\) and \(y\) intercept of a tangent to any point on the
hyperbola always has a constant area.
This property of moving along some path while while guaranteeing some initial
property of the problem stays constant: is known as a Locus.