The nine-point conic theorem is a generalization of the well-known nine-point circle theorem. In this generalization, the role of the orthocenter of the triangle \(ABC\) is taken over by any point \(P\) in the plane of the triangle, which does not belong to the lines joining the vertices of the triangle. The claim is that there is a conic that passes through the following nine points: the midpoints of the sides of the triangle, the midpoints points of the segments joining \(P\) to the vertices of the triangle and the points where the lines joining \(P\) to the vertices intersect the opposite sides. The first proof consists of the application of an affine transformation which maps an appropriately chosen triangle and its orthocenter to the points \(A\), \(B\), \(C\) and \(P\). The required conic is then obtained as the affine image of the nine-point circle. Furthermore, applying the analytical method in the real affine plane, it is proven that the nine-point conic is the locus of centers of the conics belonging to the pencil determined by the quadrilateral \(ABCP\). In the third, most comprehensive chapter, previous assertions are interpreted and generalized in terms of projective geometry. To this purpose, it is necessary to apply a number of concepts and key results of projective geometry. The locus of centers of conics belonging to a pencil is replaced, more generally, by the polar conic associated to any line \(p\) with respect to the observed pencil of conics. The polar conic may be incident with two more prominent points of the line \(p\), thus becoming the eleven-point conic. The classical nine-point circle theorem then follows in the special case when these two points are the so called absolute points of the real projective plane.