50 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



2.425 Radius of curvature of hyperbola, 



(eW - a^ 



p= ST 



angle F'PT = angle FPT. 

 angle FPN = co = | - FPT. 



angle F'PN = co'= - + F'P7\ 



fley 

 tan co = - 



2 I I 



p cos co = JP ~ F'P 

 Coordinates of center of curvature, 



Equation of Evolute of hyperbola, 



Gt-ffl- 



2.426 In a rectangular hyperbola b = a; the asymptotes are perpendicular to 

 each other. Equation of rectangular hyperbola with asymptotes as axes and 



origin at O: 



a? 

 xy--. 



2.427 Length of arc of hyperbola, 



b 2 C^ sec 2 <j> d<j> A _ i fk aey 



aejo Vi k 2 sin 2 </>' e b 2 



2.428 Polar Equation of hyperbola: 



i * w /\ 



e cos i 



r = OP, 6 = XOP, r 2 = r^ . 



e 2 cos 2 - i 



2.429 Equation of right-hand branch of hyperbola in terms of p, the perpen- 

 dicular from F upon the tangent at P and r, the radius vector FP, 



p 2 ~ r a' 

 I = semi latus rectum. 



