200 A. Mukhopadhyay — Elliptic Functions and Mean Values. [No. 2, 



tlie coordinates (a, of P, the point of intersection of the two curves, 

 is easily found, viz., 



Hence, if >)/ be the angle which the central radius vector OP makes with 

 OB, vrhich is the axis of x, we have 



sm 0/ = = - { ) 



^ a a Vr2 -h^J 



Now, the whole ai'ea common to the two curves is 



4.QORP = 4 (sector POR + sector POQ). 



But 



sector POR = hj-H = - sin - M » /" 



Again, from the equation of the ellipse, 



we have the polar equation 



80 that 



sector POQ = | j ^ p^de 



mih ah f 



But it is easy to prove tliat 



