GEOMETRY 43 



2.282 If the equation of the curve is given in the form, 



r-/(*) 

 where s is the arc measured from a fixed point of the curve, 



v-sr 



(Pr 



2.283 If p is the perpendicular from the origin upon the tangent to the curve, 



dr 

 P= r dp 



2.284 If u = - 



dtp 



2. p = p + 



2.285 ' " ' " ' dp 



2.286 Polar coordinates of the center of curvature, n, 0ii 

 fdrV d?r\* fdrV(/dr\ z 



(A-'m + U)|y +r * 



r? = 



+ 2 



0i = + x, 



/_^Y + r> 



\dd ' d0 



tanx = 



rl ^; 



2.287 If 2C is the chord of curvature (2.225): 



dr p 

 = _ = 



2.290 Rectilinear Asymptotes. If r approaches oo as approaches an angle a, 

 and if r(a - 6) approaches a limit, b, then the straight line 



r sin (a -.6) = b 

 is an asymptote to the curve r =/(0). 



