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Practice 10-6

Translating Conic Sections

Identify the conic section represented by each equation by writing the equation in standard form. For a parabola, give the vertex. For a circle, give its center and radius. For an ellipse or hyperbola, give its center and foci. Sketch the graph. 

1. 3x2 + 6x + 5y2 - 20y - 13 = 0
3. x2 + 4y2 + 8x - 48 = 0 
5. x2 + y2 + 6y - 27 = 0
7. 16x2 - 96x - 9y2 + 36y - 36 = 0
9. x2 + 2x + y2 + 14y - 31 = 0
11. 4x2 - 16x + 4y2 - 16y - 4 = 0
13. x2 - 10x + y2 + 4y - 7 = 0
15. x2 - 2x - y + 3 = 0
17. x2 + 8x + y2 + 2y + 1 = 0
19. y2 + 2y - x + 3 = 0
 2. x2 - 9y2 + 36y - 45 = 0 
 4. x2 + y2 - 8x - 4y + 19 = 0 
 6. x2 - 10x - 4y2 + 24y - 15 = 0 
 8. 10x2 + 10y2 - 70 = 0
10. 25x2 + 50x - 9y2 - 18y - 209 = 0
12. x2 + 4y2 - 4x + 8y = 0
14. x2 + 2x + y2 - 10y - 38 = 0
16. x2 + 6x - y + 7 = 0
18. x2 -y2 -4=0
20. x2 - 4x + 3 - y = 0
Write an equation of a conic section with the given characteristics.
21.	circle with center (-4, 5), radius 6
22.	hyperbola with center (-4, 5), one vertex (-4, 7), one focus (-4, 8)
23.	Points on the hyperbola are 96 units closer to one focus than to the other. The foci are located at (0, 0) and (100, 0).
24.	parabola with vertex (1, -2), x-intercept 3, and opens to the right
25.	ellipse with center (0, 2), horizontal major axis of length 6, minor axis of length 4
26.	ellipse with center (-4,-5), endpoints of major and minor axes (-4, -7), (-4, -3), (-1, -5), (-7, -5)
27.	circle with center (-1, 2), diameter 12
28.	parabola with vertex (-1, 5), y-intercept 4, and opens downward
29.	hyperbola with vertices (0, 2) and (4, 2), foci (-1, 2) and (5, 2)
30.	ellipse with center (2, -5), one end of each axis (2, -9) and (-3, -5)
31.	Points on the hyperbola are 12 units closer to one focus than to the other. The foci are located at (0, 0) and (250, 0).
32.	ellipse with center (0, -2), vertical major axis of length 5, minor axis of length 3
21.