412 ANSWEHS 



co-y lS =-L; 

 \/8 



, 

 Vtt 



C08/5 S = 0, 00871=-. 

 A*t Pi 



10 CM!, 2). 11. a = /J = -y = Cr-L. 12. 



V8 

 Page 352. Examples on Chapter II. Part II. 



1. Two coincident planes parallel to the yz-plane and at the distance + 3 

 from it. 



2. A plane parallel to the yz-plane and at the distance - 2 from it. 



3. Two coincident planes parallel to the z-axis and intersecting the 

 jry-plane in the line x y + 1 = 0. 



4. Two planes intersecting in the z-axis, and intersecting the xy-plane in 



5. Hyperbolic cylinder with generators parallel to the ar-axis. 



6. A parabolic cylinder with generators parallel to the axr 



7. A circle whose plane is parallel to the xz-plane and whose equation 



8. A pair of lines respectively parallel to y = x. 



9. The projection of this curve upon the x-plane is the hyperbola 

 3 je 2 z*+6=0, and its projection on the yz-plane is the ellipse 3 y*+4z 2 =32. 



10. For z = 6, the point (0, 0, 6) ; for z = 6 it is a circle parallel to the 

 ary-plane, and whose equation Is 9x 2 + 9 y 2 = 100. 



11. Solved like No. 9. 12. x* + y* = 25 ; * a + 4^ = 25; $- + 4= 25. 

 13. Solved like No. 12. 14. y 2 + z* + 6 x ^ 3. 

 15. (y_3)2 = 25(x + * 2 ); vertex =(0, 3, 0). 



* 1 + *V*Ul. n. L.:rjr + *- = i. 18 . 



2 7 9 



19. 16 a? 9 y* 9 z* = 1. 20. r 2 -f y 2 + 2 = 6 x. 



Page 364. Examples on Chapter HI, Part II 



1. * + = 4, f = -J. 2. r + y-f-2r = 6. 3. I ~ 1 =J^l2 



V3 * 



4. y = 2 (on zy-plane), y = 2 (on y^-plane), x + z 4 (on zz-plane) ; it 

 pierces the zy-plane at (4, 2, 0), the yz-plane at (0, 2, 4), and IB parallel t- 

 the zz-plane. 



x-\ y-2 g 8. 

 6 ' = 1 = ~J 



