2. A collection of points satisfying a geometric property can also be referred to as a ______ of points.

3. A ____________ is the set of all points (x, y) in a plane that are equidistant from a fixed point, called the center.

4. A/n ____________ is the set of all points in the plane that are equidistant from a fixed point F(called the focus) and a fixed line l (called the directrix).

5. A/n ___________ is the set of all points in the plane the sum of whose distances from two fixed points F₁ and F₂ is a constant.

6. A/n ____________ is the set of all points in the plane, the difference of whose distances from two fixed points F₁ and F₂ is a constant.

7. 6x²+12x+6y²-8y=100 is an example of a

8. 4x²+12x+y²-8y=64 is an example of

9. 6y= 3x²-15 is an example of

10. 2x²+87x-25=y²+4y is an example of

11. 6x²-15x=3y²+4y+13 is an example of

12. A hyperbola is the only conic that has

 $\frac{x^2}{4}-\frac{y^2}{25}=1$  has a major axis of length

 $\frac{\left(x+3\right)^2}{9}-\frac{\left(y-2\right)^2}{4}=1$  Use this  to answer 14 to 17

14. The center is at _________?

 $\frac{\left(x+3\right)^2}{9}-\frac{\left(y-2\right)^2}{4}=1$ 
15. The vertices are _________?

 $\frac{\left(x+3\right)^2}{9}-\frac{\left(y-2\right)^2}{4}=1$ 
16. The foci are at _________?

 $\frac{\left(x+3\right)^2}{9}-\frac{\left(y-2\right)^2}{4}=1$ 

17. The length of the major axis is ___________?

18. The standard form of 9x^2-4y²=36 is

19. The earth’s orbit is an ellipse with the sun at one of the foci. If the farthest distance of the sun from the earth is 105.5 million km and the nearest distance of the sun from the earth is 78.25 million km, find the eccentricity

of the ellipse.

20.  $\frac{x^{2\ }}{9}-\frac{y^2}{16}=1$  will have a  minor and major axis with length _____ (In that order)

21. Which of the following shows the correct graph of the circle?

22. Which graph represents the equation $x^2-10x+y^2=-9$  ? 

23. What is the focus and vertex of the parabola $\left(y-2\right)^2+16\left(x-3\right)=0$  

24. Find the equation of the parabola with vertex at (5, 4) and focus at (-3, 4).

25. Find the center and foci of the ellipse $\frac{\left(x+5\right)^2}{5}+\frac{\left(y+9\right)^2}{9}$  .

26. Find the center and vertices of the ellipse  $4x^2+9y^2-24x+72y+144=0$  

27. Which of the following shows the correct graphical representation of the ellipse $\frac{x^2}{16}+\frac{y^2}{4}=1$  

28. What are the vertices and asymptotes of the hyperbola  $9y^2-16x=144$  

29. Find the center and vertices of the hyperbola $11x^2-25y^2+22x+250y-889=0$  

30. Find the standard form of the equation of the hyperbola with the given characteristics, vertices: (0,-6), (0,6) and foci (0,-7), (0,7).

Write the equation of the ellipse that has its center at the origin with focus at (0,4) and vertex at (0, 7).

 $9x^2-9y^2=81$  

32. What is the graph of the hyperbola

33. An arch 20 meters high has the form of parabola with vertical axis. The length of horizontal beam placed across the arch 9 meters from the top is 60 meters. Find the width of the arch at the bottom.

34. A spotlight in a form of a paraboloid 9 inches deep has its focus 3 inches from the vertex. Determine the radius of the opening of the spotlight.

35. A bridge is supported on an elliptical arch of height of 7 meters and width at the base of 40 meters. A horizontal roadway is 2 meters above the center of the arch. How far is it above the arch at 8 meters from the center?

36. Which of the following item illustrates a sequence?

37. Which of the following item illustrates a series?

38. What kind of sequence is 5, 7, 9, 11, 13?

39. Find the 7th term of the sequence 1, 2, 6, 24, ...

40. What kind of sequence is 1, 5, 25, 125, 625?

41. Find the least positive two-digit term of the sequence

−18, −14, −10, −6, ...

42. If x + 2, 3x + 1, 6x – 2 form an arithmetic sequence, what is x?

43. What kind of sequence is 1, 1, 2, 3, 5, 8, 13, 21, ...?

44. What kind of sequence is

45. Find the sum of the arithmetic series: 8, 12, 16, 20, 24, 28, 32, 36

46. If 2x + 3x + 4x + 5x + ... + 41x = 1,720, what is x?

47. How many boxes of milk are needed in Gaisano grocery store display

if they want to set up a stack of 15 boxes at the base of the triangle and

one box at the top?

48. Express the sum using sigma notation: – 3 + 8 – 17 + 32

49. Evaluate the sum of 

50. Evaluate

51. Express the sum  $2+\frac{3}{2}+\frac{4}{3}+\frac{5}{4}+\frac{6}{5}$  using sigma notation

52. For the series $\Sigma_{\left(n=1\right)}^84n$  , find the number of terms in the series.

53. For the series $\Sigma_{\left(n=4\right)}^9\left(n+1\right)$  , find the number of terms in the series.

54.For the series $\Sigma_{\left(n=4\right)}^5\left(-4n\right),\$  find the first and the last term. 

55. For the series $\Sigma_{\left(n=1\right)}^5\left(n+4\right)$  , find the first and the last term.

56.Use summation notation to write the series 49 + 54 + 59 + ... for 14 terms.

57. Use summation notation to write the series 2 + 4 + 6 + 8 + ... for 10 terms.

58. Use summation notation to write the series 6.6 + 15.4 + 24.2 + ... for 5 terms.

59.Expand  $\Sigma_{\left(n=0\right)}^{\infty}2n$  

25. Find the sum of notation $\Sigma_{\left(n=0\right)}^4\left(8.8n-2.2\right)$