2D projections of n-D hyper-ellipsoid in matrix representation

Question

I have a hyper-ellipsoid defined as the transformation of the unit ball:

$$ \mathcal{E} = \left\{ T x + d \mid \left\Vert x \right\Vert_2 \leq 1 \right\} $$

where $T \in \mathbb{R}^{n \times n}$ is symmetrical and positive definite and $d \in \mathbb{R}^{n}$.

Now I want to plot the 2D projections of this ellipsoid ($x_1-x_2, x_1-x_3, x_2-x_3$, etc.)

How exactly do I do this?

Thanks for your help!