10 Frank Jone s using x(s) + t(p(s) an d y(s) - f ttp(s). W e tak e th e derivativ e o f th e quotient o f th e correspondin g A an d L 2 , an d the n se t t 0. W e obtain, symbolically , 1 dA 2AdL Thus, a t t = 0, L2 dt L 3 d t dA d L ~dt ~ ~dt 0. Therefore, jus t a s in th e calculation s don e i n sectio n B , we have 1 fs° - / (xip f + y V ~ w ' ~ # 0 d s 0 =x r^M ds . Jo y^Ty^ Integrating b y parts produce s 1 f s ° 2 Jo Jo ¥ + y/x'2 + y'2l \ yV 2 + y' 2 M ds. The fundamenta l lemm a no w gives -a:' = - A V X 7 \ y V 2 + 7/ /2 One integratio n the n give s x c\ = A y^/2_| _ y/2 ' y - c 2 = -A - y/xf2 + y f2 But the n w e see tha t (x-c1)i + (y-c 2 )2 = X 2 , so our curv e i s a circle!
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