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# Analytic Geometry Chapter Exam

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. What are the three direction ratios for the vector with coordinates (2, 7, 1)?

#### Question 2 2. What is the magnitude of the vector with coordinates (34, 56, 21)?

#### Question 3 3. Which of the following statements is true about an ellipse and/or hyperbola?

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Question 4
4.
Given that *F* and *G* are the foci of the hyperbola shown, which of the following statements is true?

#### Question 5 5. Find the equation of the plane passing through the points P(1,1,1), Q(2,2,2), and R(3,3,3).

### Page 2

#### Question 6 6. Find the equation of the plane passing through the points P(2,2,0), Q(3,2,1), and R(1,3,1).

#### Question 7 7. Write the Standard Form of the equation for a circle centered at point (4 , 6) and has a radius of 10.

#### Question 8 8. Write the Standard Form of the equation for a circle centered at point (-2 , -8) and has a radius of 4.

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Question 9
9.
The equation of a line is *y* = -.75*x* + .5. Find the distance from a point (1,2) to this line using the formula

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Question 10
10.
The equation for a line is *y* = -3*x* + 4. What is the slope?

### Page 3

#### Question 11 11. A bird flies from the point (1, 2, 3) to the point (3, 2, 1). If each unit is a mile, what is the distance between these two points? Use two significant figures in your answer.

#### Question 12 12. Calculate the distance between (1, -2, 4) and (-1, 2, 4). Express your answer using 2 significant figures.

#### Question 13 13. Which is the parametric form for an ellipse?

#### Question 14 14. What is the eccentricity of a circle?

#### Question 15 15. What do you get when you graph a linear equation in the coordinate space?

### Page 4

#### Question 16 16. Which direction do you go if your z component is negative?

#### Question 17 17. Which of the following describe a plane

#### Question 18 18. Which of the following statements are true?

#### Question 19 19. What is the surface area of a sphere with a radius of 1 ft? (Use 3.14 for pi and round your answer to the nearest tenth.)

#### Question 20 20. What is the volume of a sphere with a diameter of 4.5 mm? (Use 3.14 for pi and round your answer to the nearest tenth.)

### Page 5

#### Question 21 21. What is the measure of the acute angle formed from the intersection of a line with a slope of 1 and another line with a slope of 3?

#### Question 22 22. What is the angle of inclination of a line with slope 1?

#### Question 23 23. What is a unit vector?

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Question 24
24.
Given that *FP* + *GP* is constant for all *P* on the ellipse shown, which of the following statements is true?

#### Question 25 25. Find the equation of the plane passing through the points P(-1,2,-3), Q(4,-5,6), and R(-7,8,-9).

### Page 6

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Question 26
26.
Convert the equation for a circle from General Form to Standard Form:

x^2 + y^2 - 12x + 14y + 60 = 0

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Question 27
27.
If the equation of a line is *y* = -3*x* + 4, what is the slope of a line perpendicular to it?

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Question 28
28.
The *x*-*y*-*z* coordinates of the origin in a three-dimensional space are _____.

#### Question 29 29. Which of the following is NOT a conic section?

#### Question 30 30. Which variables do you set to 0 when you need to find the y intercept?

#### Analytic Geometry Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!