Its cartesian equation, when the line joining the two fixed points is the axis of x and the middle point of this line is the origin, is (x 2 + y 2)2 = 2a 2 (x 2 - y 2) and the polar equation is r 2 = 2a 2 cos 20.
The polar equation is r= I -f - 2 cos 0 and the form of the curve is shown in the figure.
The polar equation of the cross-section being rI cos 19 =al, or r + x = 2a, (3) the conditions are satisfied by = Ur sin g -2Uairi sin IB = 2Uri sin 10(14 cos 18a'), (4) 1J/ =2Uairi sin IO = -U1/ [2a(r-x)], (5) w =-2Uaiz1, (6) and the resistance of the liquid is 2lrpaV2/2g.
The polar equation is r=a+b cos 0, where 2a= length of the rod, and b= diameter of the circle.
This is recognized as the polar equation of a conic referred to the focus, the half latus-rectum being hf/u.