construct the conic. ("To construct the conic" means here to construct as
many other points as may be desired.)

6. Given three points on the conic, and the tangent at two of them, to
construct the conic.

7. Given five points, two of which are at infinity in different
directions, to construct the conic. (In this, and in the following
examples, the student is supposed to be able to draw a line parallel to a
given line.)

8. Given four points on a conic (two of which are at infinity and two in
the finite part of the plane), together with the tangent at one of the
finite points, to construct the conic.

9. The tangents to a curve at its infinitely distant points are called
its _asymptotes_ if they pass through a finite part of the plane. Given
the asymptotes and a finite point of a conic, to construct the conic.

10. Given an asymptote and three finite points on the conic, to determine
the conic.

11. Given four points, one of which is at infinity, and given also that
the line at infinity is a tangent line, to construct the conic.





CHAPTER V - PENCILS OF RAYS OF THE SECOND ORDER