406 XtfMr; 



Pages 204, 205. Art. 123 



i Tm, 2. 



8 *i* + ti* = i ; gi*-*ig = g i 

 + 



a' 



6. r,x = 2p(y + y,-10)c 2px + x iy = *,(2f> + y,). 

 6. 3(ri + 4)x-6y!y + 12xi = 0; 6yiX -- :5(z, + 4)y = 4 yi 

 7 1 -3)x + 10(y l + l)y = 3x 1 ~10y 1 -|-8; 10(yi + l)x- 



= 10 xi -t- 8 XM -I- 3 yi. 



8. JW = 2p(x + Xi). 9. (x 1 -4)x + 2(2y i + 5)y = 4r, - K>y,. 



10. y = 1 ; x + 2 = 0. 11. .'3 x + L' y = ; 2 x - 3 y = 0. 



IS. x + y + 4 = 0;y = x + 2. 13. x + >/8y = 4;y:^ 



14. 3x-2y = 8 



Pages 208, 209. Art. 126. 



1. Chord of contact : 2 x + y = 1 ; points of contact : (~1, .'5), (-2, 6); 

 equations of tangents : 4x-fy+l = 0, x + y = 3. 



4. x + 4y = 27;Ye. 5. 2y-j-9x = 0; 2y + 3x = 0. 



6. y-l=(-| T VVT02)(x-f 1). 8. y-2= 6 *v^(x-3). 

 9. The four normals are : y 2 = and y V6 (x 1 ). 



Pages 212. 213. Art. 129. 



1. x-2y = 6. 



2. x-2y = 6; (~4 2 VT6, J6 VT6) ; 



(6 T 2VT6)x -(10 T 2Vl5)y 2VT6 = 0. 

 6. x-8y+19=0; yes. 7. tan-(|). 8. It is. 9. x-3y+9=0. 



Pages 216-218. Examples on Chapter VIII. 

 1. 4y = VlOx + 4. 

 2 03x--32y = 144; 63x-f 32y = 12\/506. 



4. 0.z + 0-y + ABC-AF*-BG* = Q', cf. Art. 60, p. 05. 



6. The foci: (2\/6, 0). 



6. The directrix x=- ; x 4- my=ae ; they are perpendicular to each oth< r. 



7. It is the tangent at the vertex. 8. x = 3, y 3 = 0. 



10. The directrix. 11. The focus. 12. At infinity ; at infinity. 



