The nodal circle which bisects the angle between the line drawn from any point on a cardioid to the cusp and the nodal circle through the point which cuts the director circle orthogonally, is a tangent circle at that point. The latus rectum of a parabola is equal to four times the distance from the focus to the vertex. The latus rectum of a cardioid is equal to its length on the axis. If a tangent to a parabola cut the axis produced, the points of contact and of intersection are equally distant from the focus. If a nodal tangent circle cut the axis of a cardioid, the points of intersection and of tangency are equally distant from the cusp. If a perpendicular be drawn from the focus to any tangent to a parabola, the point of intersection will be on the vertical tangent. If a nodal circle be drawn tangent to a cardioid, the diameter of such circle passing through the cusp will be a common chord of this circle and another described on the axis of the cardioid as diameter. The directrix of a parabola is the locus of the intersection of tangents that cut at right angles. The base circle is the locus of the intersection of nodal circles tangent to a cardioid, which cut orthogonally. The circle described on any focal chord of a parabola as diameter will touch the directrix. The circle described an any nodal chord of a cardioid as diameter will be tangent to the base circle. The locus of a point from which two normals to a parabola can be drawn making complementary angles with the axis, is a parabola. The locus of the point through which two nodal circles, cutting a cardioid orthogonally, and making complementary angles with the axis, can be drawn is a cardioid. Two tangents to a parabola which make equal angles with the axis and directrix respectively, but are not at right angles, meet on the latus rectum. Two nodal circles tangent to a cardioid which make equal angles with the axis and latus rectum, respectively but do not cut orthogonally intersect on the latus rectum. The circle which circumscribes the triangle formed by three tangents to a parabola passes through the focus.