Brief Course in Analytic Geometry

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25x2-100;+ 1 = 0. 4. aa?=bxy-cy\ 2. 2^^ + 40; = 0. 5. a?-\-^-i:X — A = Q.
3. x'-2xii+y'^+Sx-Zy=zQ. ' 6. ar' + 92/ = 9.
What are the curves of intersection of the surfaces represented by the equations : 7. a;-l = 0, z^ + y^ + «' = VQ'{ 8. 4ar'-92/' = 0, z = 4?
9. x' + y^-^z' = ^, iaP + y'' = 4:?
10. Qiaf + y')- z'' = 25-10 z, « = ±5?
11. Sx'-iy^-z'^n, ^ + t=l?
■^ ' 9 16 Determine the traces upon the coordinate planes of the folloW' ing surfaces : 12. x' + y' = 4:z'; 13. x' - 3y' + 2z'' = 6.
145]
... THE LOCUS OF AN EQUATION. SUB FACES 243 Find the equation of : 14. The paraboloid of revolution one of whose traces is 15. The cone of revolution one of whose traces is « = y — 10 and whose axis is the axis of y. Find its vertex.
16. The oblate spheroid one of whose traces is x "^ o' ~ ■'"■ L o 17. The prolate spheroid one of whose traces is 7 9 18. The surface of revolution whose axis is the avaxis and one of whose traces is y^x = — 4.
19. The hyperboloid of two nappes one of whose traces is 162/''-9a^ = 144.


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