[SOLVED] How to check a point is inside an ellipsoid with orientation?

For an ellipsoid of the form

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

with orientation vector $\vec{r}$ and centre at point $\vec{p}$ , how to find whether a point $\vec{q}$ is inside the ellipsoid or not?

An additional note that the geometry actually is with a=b (spheroid) and therefore one axis is sufficient to define orientation

Note: I see a similar question asked in the forum. But, it is about an ellipsoid at origin and without any arbitrary orientation and here both arbitrary position and orientation are considered.

Find affine transform M that translates this ellipse in axis-oriented one (translation by -p and rotation to align orientation vector r and proper coordinate axis).
Then apply this transform to point p and check that p' lies inside axis-oriented ellipsoid, i.e.
x^2/a^2+ y^2/b^2+z^2/c^2 <= 1