In Exs. 19-24, find the points of in tersection and trace the curves. 19. z 3y, 3z +- y-24y +36 = 0. Ans. (+3, 3), (±6, 12). Ans. (4, 4), (1, 2). %3D %3D 20. y 4z, 4r + 9y² = -112 8z +72y %3D %3D 21. z =y+ 10, ya + 5(z – 1)² == 81. %3D - Ans. (-3,-1), (-2,-6), (1, -9), (4, 6). 448. Ans. (-3, +8), (4, ±6). Ans. (0, 0) twice. Ans. (0, 0) four times. 2. 4z y = 100, 4(z +3) + 7y = 4az. %3D %3D 23. z + y + 4az 24. z2 + - 0, 2z2 +y %3D %3D 4ar = 0, 2r? + y? = slar.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 1E: Does a right circular cylinder such as an aluminum can have a symmetry with respect to at least one...
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Number 24
The center is at (2, -1), major axis par-
allel to Oy, semi-axes a =,b = 1, distance
from center to foci Va?-6 = v=}V5,
Istus rectum =
Figure 95
Exercises
Te Ers. 1-18, find the center and foci, plot the ends of the axes and of the
laters recta, and di aw the curve.
1.
25
(z - 2)
-1)3
= 1.
6.
(z - 4) (v +2)*
2.
4.
6.
- 1.
(z+ 1)
(y - 3)3
= 1.
(z + 5)* (y – 4)*
3.
4.
1
1
= 1.
(z+ 2a)
(z+ a) (y- 2a)
= 1.
5.
= 1.
6.
a?
2a2
7. z+ 2y1-6z +.5 0.
9. z + Vy +3z- 1. 8y+9 = 0. 10. z + 2y2 + 4x - 12y + 16 = 0.
4a2
8. z+ 9y+ 18y = 0.
11. 2z+ y - 4x - 2 1.
12. 3+ 2y
13. 3z + y 6cz.
14. z+ 4y
15. 16z + 12y -12y-9 0.
16. 7z+ 2y +- 14z-8y+1= 0.
17. 3z+4y -
18. 9z + 10y - - 90z -
36z -
16y +134 0.
=: 4cy.
18z + 8y + 19 = 0.
40y + 175 = 0.
In Exs. 19-24, find the points of in tersection and trace the curves.
19. z 3y, 3z + - y-24y + 36 = 0.
20. y= 4x, 4r + 9y² = 8z + 72y -119
21. z =y+10, ya+ 5(z - 1)² == 81.
Ans. (+3, 3), (±6, 12).
Ans. (4, 4), (1, 2).
%3D
%3D
Аns. (-3, - 1), (-2, - 6), (1, — 9), (4, 6).
22. 4z y = 100, 4(z+ 3) +73 = 448. Ans. (-3, ±8), (4, ±6).
= 4ar.
%3D
0, 2z + y? :
0, 2z2+ y² = laz.
25. A circle is tangen t to the circles z + y² = 4, z + y 12y + 64.
23. z+y+ 4az
24. 2 +y - 4az =
Ans. (0, 0) twice.
Ans. (0, 0) four times.
end the locus of its cenyiter and draw the figure.
Ans. 4z + 31 v-18y-81 == 0; 16z² + 7y-42y-49 = 0.
Transcribed Image Text:The center is at (2, -1), major axis par- allel to Oy, semi-axes a =,b = 1, distance from center to foci Va?-6 = v=}V5, Istus rectum = Figure 95 Exercises Te Ers. 1-18, find the center and foci, plot the ends of the axes and of the laters recta, and di aw the curve. 1. 25 (z - 2) -1)3 = 1. 6. (z - 4) (v +2)* 2. 4. 6. - 1. (z+ 1) (y - 3)3 = 1. (z + 5)* (y – 4)* 3. 4. 1 1 = 1. (z+ 2a) (z+ a) (y- 2a) = 1. 5. = 1. 6. a? 2a2 7. z+ 2y1-6z +.5 0. 9. z + Vy +3z- 1. 8y+9 = 0. 10. z + 2y2 + 4x - 12y + 16 = 0. 4a2 8. z+ 9y+ 18y = 0. 11. 2z+ y - 4x - 2 1. 12. 3+ 2y 13. 3z + y 6cz. 14. z+ 4y 15. 16z + 12y -12y-9 0. 16. 7z+ 2y +- 14z-8y+1= 0. 17. 3z+4y - 18. 9z + 10y - - 90z - 36z - 16y +134 0. =: 4cy. 18z + 8y + 19 = 0. 40y + 175 = 0. In Exs. 19-24, find the points of in tersection and trace the curves. 19. z 3y, 3z + - y-24y + 36 = 0. 20. y= 4x, 4r + 9y² = 8z + 72y -119 21. z =y+10, ya+ 5(z - 1)² == 81. Ans. (+3, 3), (±6, 12). Ans. (4, 4), (1, 2). %3D %3D Аns. (-3, - 1), (-2, - 6), (1, — 9), (4, 6). 22. 4z y = 100, 4(z+ 3) +73 = 448. Ans. (-3, ±8), (4, ±6). = 4ar. %3D 0, 2z + y? : 0, 2z2+ y² = laz. 25. A circle is tangen t to the circles z + y² = 4, z + y 12y + 64. 23. z+y+ 4az 24. 2 +y - 4az = Ans. (0, 0) twice. Ans. (0, 0) four times. end the locus of its cenyiter and draw the figure. Ans. 4z + 31 v-18y-81 == 0; 16z² + 7y-42y-49 = 0.
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