English is not my native language and I'm neither a mathematician nor a statistican by trade so please excuse me if I fail to explain my problem in a concise way.
I'm trying to visualize a multivariate reference region of normally distributed measurements. A multivariate reference region can mathematically be described as an $n$-dimensional ellipsoid of the form: $$ (x-cx)'A(x-cx)=1 $$ where $cx$ is a $n \times 1$ vector representing the center of the ellipsoid and where the eigenvectors and eigenvalues of $A$ ($n \times n$ pos definite matrix) contains information on the orientation and semiaxis of the ellipsoid (wiki).
In order to present this I would like to plot the 2D intersection ellipse when $n-2$ positions of the vector $x$ is known. In the above equation $A$ and $cx$ will also be known.
Example: Let's say I have an multivariate reference region ($A$ and $cx$ known) for age, systolic blood pressure and diastolic blood pressure ($n=3$). Then I would like to plot the ellipse describing what systolic and diastolic blood pressure could be expected in subjects with the exact age of $60$ for instance. Then the vector $x=(60, s, d)$ where $s$ and $d$ are the unknowns describing the ellipse I want to visualize.
With the help of this article I've managed to find the orientation and dimensions of the 2D intersection ellipse of a 3-dimensional ellipsoid. It is, however, beyond me to generalize the solution into $n>3$ dimensions. One aspect that might simplify the problem is that the intersection plane will be perpendicular to the axes of the coordinate system.
Suggestions? Solutions? Anyone?