# Tikz plot - set origin for plots

I am trying to position a parametric curve within a tikzpicture.
Using the following code, I the curve is plotted with the centre at (0,0), but I would like the centre to be positioned at (0,5) so that the parametric curve touches the circle. I've looked up plot in the tikz documentation; using \addplot from pgfplots; positioning at nodes and paths, all to no avail, the curve remains with centre (0,0)

\documentclass{standalone}

\usepackage{tikz}

\begin{document}
%
\begin{tikzpicture}
%
%
\draw [domain=0:360, samples=300] plot ({-5 * sin(\x) * (sin(\x/2))^1.2 }, {-5 * cos(\x)});
%
\end{tikzpicture}
%
\end{document}

How can I specify where the centre of the plot is?

Solution 1: Add (0,5) to the plot (note the number 5 starting the y coordinate of the plot).

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw [domain=0:360, samples=300]
plot ({-5 * sin(\x) * (sin(\x/2))^1.2 }, {5-5 * cos(\x)});
\end{tikzpicture}
\end{document}

Solution 2: Shift the center of the circle down by 5.

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw [domain=0:360, samples=300]
plot ({-5 * sin(\x) * (sin(\x/2))^1.2 }, {-5 * cos(\x)});
\end{tikzpicture}
\end{document}

Solution 3: Use a scope and shift its contents, either the circle or the plot.

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}