410 ANSWERS 



7. Cx + 8xy-3y-3lx-10y-180 = 0. 



8. Jx + y = t x-y=l; 2 x a - xy - y* - 2x - y + 6 = 0. 



9. 3x-f y + 2 = 0, x+lly = l. 10. Ox'- 16y' + 30x + 160y r= 



Pages 283, 284. Art. 170. 



8. 2V5, 2\/2; v/2 ; (2, 2), (-2, -2). 

 $ 2\/3), (~2V3, -2V^; (4>/3, 4\/3), (-4V3, -4\/3). 



Page 287. Art. 172. 



1. lfly = 3x; y = 3z. 2. y = x; 16y = 0ac. 3. 16y 



4. 8/-3yr 



Pages 289-291. Cxaiuples on Chapter XI. 

 1. **-3y*=16. 2. 15y=16z; (4, y), ("4, - 



4. -- ^ = 1, if the middle point of the base is the origin and the 



a 1 c 2 - a* 

 base of the triangle on the x-axis. 



6. 2xy = (c* x 2 ), if k is the constant and axes chosen as in Ex. 4. 



6. sin-jf-^- j, where a', 6' are the conjugate semi-diameters. 

 \a'v'J 



11. xy + 3x 2y = 0. 



15. (-4, -3); 2J. 16. Oy-5x = 7. 18. 8v^y 4x = 3V7. 



19. The four normals are : 



Vl76(4y-3x+l) + 300 = 0, vT75(4y + 3x - 17)-|- 300 = 0. 



24. Vb* + abx Va a - ab y Vab(a* -f ^ ) = 0. 



25. 32y^(V328l41)x. 29. x + y = v^MT6 ; f q * t _r y \ 



Wa<+& \^T^^ 

 30. x = 2,y = 3; xy - 3x - 2 y + 12 = 0. 



81. 3x-f 2y + 4 = 0; 3x*4-2xy-f 4x + = 0. 



Pages 296, 297. Art. 176. 



1. Centers (0, v/2); foci = (V6, V2\/6); axes: y-x = M', 

 V2; directrices: x + y 



