322 A. Miikliopadbjay — Differential Equation of all Paraholas. [No. 4, 



\ (to) / do)^ 









V 



'-(Q' ' 



Tlierefoi 



e, from 





R = 



do) 

 = p cos . -_— , 

 dip 



we have 



easily the 



relation 









R = 



3p^ 



9p2 . 





We can now, without much difficulty, change the variables, and 

 thus obtain an expression for R in terms of cc and y. Thus, as we have 

 already seen 



(1 + /)^ 



P = 



dp ^ a±f} 



dx (f 



dm q 



I Sp^'-r (1 -f f') 



whence 



doc 1 + ^9^ ' 



Hence, we have 



] 



L 



r 3p22 — r (1 + 1^2 J 



4- 3 ^^M 3pg2 _,.(! + 



and 



^ _ d_ (dp\ _ dx^ d_ fdp\ 

 d(}fi do) \doi / d(x) dx \doi / 



(1 + p^) 



j (I + i>^) 3^* - 8p^2r ^ (1 _^ _p2) (3^^2 _ ^5) L. 9p2^4 C , 



Hence, by actual calculation, we find that 



[ 





r2 (1 + p2) - 6p^V + % 



r2). 



■1 



