Ellipsoid in n-dimension

Question

Is the ellipsoid's equation in n-dimension looks like this? https://en.wikipedia.org/wiki/Ellipsoid#Standard_equation

Like $x_1^2/r_1^2 + x_2^2/r_2^2 + ... + x_n^2/r_n^2 = 1$

Answer 1

In general, the equation of the ellipsoid in $n-$dimensions is: $\sum_{i=1}^{n}\frac{(x_i-p_i)^2}{a_{i}^2}=1$, where the centre have coordinates $P(p_1,p_2,\cdots ,p_n)$, $a_1,a_2,\cdots,a_n$ are the lenght of the semi-axis and $x_1,x_2,\cdots,x_n$ are the $n$ dimensions. I hope it has helped you.