48 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



Coordinates of center of curvature: 



Equation of Evolute of Ellipse, 



* * 



2.416 Area of Ellipse, irab. 



Length of arc of Ellipse, 



/<* _ 

 Vi - e 2 sin 2 <p dcfr. 



2.417 Polar Equation of Ellipse, 



r = F'P, 6 = angle XF'P, 



r _ a(i-e 2 ) 

 i e cos 6 



2.418 r = OP, e = angle XOP, 





2.419 Equation of Ellipse in terms of p, the perpendicular from F upon the 

 tangent at P, and r, the radius vector FP: 



r a 

 I = semi latus rectum. 



2.420 Hyperbola (Fig. 5). 



2.421 O, Center; F, F', Foci. 

 Equation of hyperbola, origin at O, 



2 _Z 2 =I 

 a 2 b 2 



x = OM, y = MP, a = OA= OA'. 



2.422 Parametric Equations of hyperbola, 



x = a cosh u, y = b sinh u. 

 or 



x = a sec 0, y = b tan <f). 



4> = angle XOP', where P' is the point where the ordinate at T meets the 

 circle of radius a, center O. 



