Edit: I've made this question more crisper. The copy-pasted content is from Paul lockhart's Measurement. Below he proves that a parallel projection of a circle onto a tilted plane (Equivalently a cross section of a sliced cylinder) is an Ellipse (defined as a dilated circle). Dilation is like streching a rubber sheet in one direction, rather than zooming in all directions.
But we know that a suitable cross section of a cone is also an ellipse.
How can we use the same line of above reasoning to prove that it is an ellipse (dilated circle) for central projection (projection lines emerging from a point, in this case the vertex of the cone, rather than from infinity) too ?
