Tracing Caustic Curves, 

 Let CSP = 6>, SC = a, CP = r, 



CPH = & NP = n = rcos<f', 



CPN = £', CN = p = rsin<£', 



CTP=^, CM=#p==^sintf>. 



259 



Ms:. 1. 



e. 



0. 







10° 10' 55" 







-45° 





 ■27° 39' 50' 



5 



4-4284 



p. 



55325 

 3-5420 



105325 

 7-9704 



p. 





 •2-3214 







4-9766 



(i.) From the figure it is seen that yjr = + <f> — <fi' . 

 (The magnitudes are considered as simple geometrical 

 quantities without any vectorial sense of direction.) 

 Differentiate (i.) with regard to i/r. 



(i'O 



d6_ M _dj>' 

 dty dty clyjr ' 



But sin(9=^ ? sin<f>=^, sin<f>' = ^. 



a T r ■ r 



d6 fjup' a d(f) fip' d<j>' p' 



:. TT - = - C£: -sec<9, -p. =^ sec</>, - 7T = 7 -sec6'. 



* ay a d-y r T ay 7' r 5 



1 r <¥ 



when » = -77 . 



1 ay 



.*. from (i'.) -7 = -sec 0+ — sec 6 sec <V, 



p\ a 



(ii) or 7/ = 



r 

 ar 



(a) 



pr sec 6 + pa sec </> — a sec <£'* 

 S2 



