10 Chapter Test

Do you know HOW?

Identify the type of each conic section. Give the center, domain, and range of each graph.

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2. 
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4. 
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Identify the focus and the directrix of the graph of each equation.

5. y = 3 x 2 y equals , 3 x squared
6. x = − 2 y 2 x equals . negative 2 y squared
7. x + 5 y 2 = 0 x plus , 5 y squared , equals 0
8. 9 x 2 − 2 y = 0 9 x squared , minus 2 y equals 0

Write an equation of a parabola with its vertex at the origin and the given characteristics.

9. focus at ( 0 , − 2 ) open 0 comma negative 2 close
10. focus at (3, 0)
11. directrix x = 7 x equals 7
12. directrix y = − 1 y equals negative 1

For each equation, find the center and radius of the circle. Graph the circle.

13. ( x − 2 ) 2 + ( y − 3 ) 2 = 36 open x minus 2 close squared . plus . open y minus 3 close squared . equals 36
14. ( x + 5 ) 2 + ( y + 8 ) 2 = 100 open x plus 5 close squared . plus . open y plus 8 close squared . equals 100
15. ( x − 1 ) 2 + ( y + 7 ) 2 = 81 open x minus 1 close squared . plus . open y plus 7 close squared . equals 81
16. ( x + 4 ) 2 + ( y − 10 ) 2 = 121 open x plus 4 close squared . plus . open y minus 10 close squared . equals 121

Write an equation of an ellipse for each given height and width. Assume that the center of the ellipse is (0, 0).

17. height 10 units; width 16 units
18. height 2 units; width 12 units
19. height 9 units; width 5 units

Find the foci of each ellipse. Then graph the ellipse.

20. x 2 + y 2 49 = 1 x squared , plus , fraction y squared , over 49 end fraction , equals 1
21. 4 x 2 + y 2 = 4 4 x squared , plus . y squared , equals 4

Find the foci of each hyperbola. Then graph the hyperbola.

22. x 2 64 − y 2 4 = 1 fraction x squared , over 64 end fraction , minus , fraction y squared , over 4 end fraction , equals 1
23. y 2 − x 2 225 = 1 y squared , minus . fraction x squared , over 225 end fraction . equals 1

Write an equation of an ellipse with the given characteristics.

24. center ( − 2 , 7 ) ; open negative 2 comma 7 close semicolon  horizontal major axis of length 8; minor axis of length 6
25. center ( 3 , − 2 ) ; open 3 comma negative 2 close semicolon  vertical major axis of length 12; minor axis of length 10

Write an equation of a hyperbola with the given characteristics.

26. vertices ( ± 3 , 7 ) ; open plus minus 3 comma 7 close semicolon  foci ( ± 5 , 7 ) open plus minus 5 comma 7 close
27. vertices ( 2 , ± 5 ) ; open 2 comma plus minus 5 close semicolon  foci ( 2 , ± 8 ) open 2 comma plus minus 8 close

Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyperbola, give the center and foci. Sketch the graph.

28. 3 y 2 − x − 6 y + 5 = 0 3 y squared , minus x minus 6 y plus 5 equals 0
29. 4 x 2 + y 2 − 16 x − 6 y + 9 = 0 4 x squared , plus , y squared , minus 16 x minus 6 y plus 9 equals 0

Do you UNDERSTAND?

30. Writing Explain how you can tell what kind of conic section a quadratic equation describes without graphing the equation.
31. Reasoning What shape is an ellipse whose height and width are equal?
32. Open-Ended Write an equation of a hyperbola whose transverse axis is on the x-axis.

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