geometrical interpretation of equation involving the quadratic form

Question

Please I need help from the experts regarding this question:

Describe the geometrical interpretation of the this equation involving the quadratic form $$ (x - \mu)'\,\Sigma^{-1}(x-\mu) = c^2 $$

Where x and μ are vectors, x represents your sample vector and μ is the mean vector. Σ is the variance/covariance matrix and c is a constant.

Any advice will be greatly appreciated.

Answer 1

This is a $p$-dimensional ellipsoid centered at $\mu$. Please see here: https://en.wikipedia.org/wiki/Ellipsoid#In_general_position for further details.