Isolines (quantiles) of bivariate normal distribution

Calculates the elliptic isolines corresponding to quantiles of bivariate normal distribution

The function returns the symbolic equation of the ellipses corresponding to the isolines of a given quantile, or the isoline and its corresponding quantile passing through a given point.
Despite common contour plots where the isoline connects points of the same density, here the isoline connects points corresponding to quantiles of the same level.

The code is based on the fact that the q-level isoline satisfies:
(X-M)'inv(S)(X-M) = -2*log(q)
with X being the bivariate normal data, S its covariance matrix, and M its mean vector.