8. Show that the poles of the tangents of one conic with respect to another lie on a conic.
9. The polar of a point A with respect to one conic is a, and the pole of a with respect to another conic is A'. Show that as A travels along a line, A' also travels along another line. In general, if A describes a curve of degree n, show that A' describes another curve of the same degree n. (The degree of a curve is the greatest number of points that it may have in common with any line in the plane.)
CHAPTER VII - METRICAL PROPERTIES OF THE CONIC SECTIONS
107. Diameters. Center. After what has been said in the last chapter one would naturally expect to get at the metrical properties of the conic sections by the introduction of the infinite elements in the plane. Entering into the theory of poles and polars with these elements, we have the following definitions:
The polar line of an infinitely distant point is called a diameter, and the pole of the infinitely distant line is called the center, of the conic.