440 
ON A NEW POEM OE TANGENTIAL EQUATION. 
145. If the bicircular quartic be a Cartesian oval, the focal conic F is a circle; and 
taking the line joining the centres of J and F as the axis of x, we may write their 
equations in the forms 
F=2 2 +^ 2 — a 2 = 0, J=(#— /) 2 +3/ 2 — ^ 2 =0, 
and we get 
§gd&=§ \/a 2 -\-f 2 — Jc 2 — 2q/'cos ; . . . . • . . (304) 
and this represents an arc of an ellipse. Hence Roberts’s and Genocchi’s theorems are 
proved. 
