94 



KANSAS UNIVERSITY QUARTERLY. 



but are not at right angles, meet respectively but do not cut ortho- 



on the latus rectum. gonally intersect on the latus 



rectum. 



The circle which circumscribes If three nodal circles be drawn 



the triangle formed by three tan- tangent to a cardioid, the three 



gents to a parabola passes through points of intersection of these three 



the focus. circles are on a straight line. 



If the two normals drawn to a If the two nodal circles cutting 



parabola from a point P make a cardioid orthogonally and pass- 



equal angles with a straight line, 

 the focus of P is a parabola. 



Any two parabolas which have 

 a common focus and their axes 



through the point P, make equal 

 angles with a fixed nodal circle, 

 the locus of P is a cardiod. 



Any two cardioids which have 

 a common cusp and their axes in 

 in opposite directions intersect at opposite directions intersect at 

 right angles. right angles. 



A number of other theorems on the limacon and cardioid are 

 given in Professor Newson's article in this number of the Quarterly, 

 and these need not be repeated here. 



