EXAMPLES. 303 



8. 4c 3 = (a + 3a?) (x* + y* ). 



r> 7, . ( x 2a \ , a 



.Kesufr. # = + ---) and = --. 

 \Va 3 v/ a 



9. (x + a)/=(y + J)cc s . 



Result. x + a = Q, y + 6 = 0, y = x + b a. 



10. (y-2#) (?/ 2 -a; 2 )-a(#-ce) 2 + 4a 2 (;c + 2/)=a 3 . 



T, 7 2a a 



.KesMft. ^ = a;, T/ -f a; = -- , y - 2x = - . 



11. ^ 2 (a; - y} z + ax* (x - y\ - Zcfy' - a 4 = 0. 



Result, y = x + ^ (1 + 



A 



12. x (x 2 - a 2 ) - 27/ (/ - a 2 ) = 3a^ 2 + a 3 . 



Result. 2 = 



1 3. cc 2 (a; - yj 2 - a 2 (ic 2 + j/ 2 ) = 0. 



Result. x = a, y = xa \/2. 

 14. 7-a; 2 ic 2 -a 2 = a 4 . 



15. / - 3y 2 x + 4 3 + ay* + axy - 600^ + 2i 2 ^ - 6 2 y + c 3 = 0. 



16. If a curve of the third degree be referred to two asymp- 



totes as axes, shew that its equation will be of the form 



xy (ax -f by + c) + ax + b'y + c' = 0, 

 and that the equation to the third asymptote will be 

 ax + by + c = 0. 



