# OAE Mathematics: Conic Sections Chapter Exam

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### Page 1

#### Question 1 1. What is the shape of a parabola?

#### Question 2 2. What do we call the highest or lowest point of a parabola?

#### Question 3 3. How do we define a parabola using its focus and directrix?

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Question 4
4.
Suppose that a parabola has focus *F* and directrix *y* = *k*. The distance from a point, *P*, on the parabola to the directrix of the parabola is 11 centimeters. How far is it from *P* to *F*?

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Question 5
5.
Suppose that a parabola has focus point *F* and directrix *y* = *k*. If the distance from *F* to a point *P* on the parabola is 7 inches, what is the distance from the point *P* to the directrix of the parabola?

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Question 6
6.
What is the equation of a hyperbola with a horizontal transverse axis such that (*h*, *k*) is its center, *a* is the distance from the center to a vertex, *c* is the distance from the center to the foci, and *b*2 = *c*2 - *a*2?

#### Question 7 7. Consider a hyperbola that has a horizontal transverse axis such that its center is (0,0), the distance from the center to a vertex is 2, and the distance from the center to the foci is 3. What is the equation of the hyperbola?

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Question 8
8.
Consider the equation of a hyperbola ((*x* - *h*)2 / *a*2) - ((*y* - *k*)2 / *b*2) = 1, where (*h*, *k*) is the center of the hyperbola, *a* is the distance from the center to the vertex of the hyperbola, and *c* is the distance from the center to the foci of the hyperbola. How do we find *b*?

#### Question 9 9. What is the definition of a hyperbola?

#### Question 10 10. Which of the following is the shape of a hyperbola?

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Question 11
11.
For a parabola given by *y* = 4(*x* - 3)(*x* - 4), the form of this equation is _____

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Question 12
12.
A parabola equation is given as *y* = 3(*x* - 2)^2 + 5. What are the coordinates of the vertex?

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Question 13
13.
When a parabola equation is written as *y* = -5(*x* -2)^2 + 6, the form is _____

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Question 14
14.
A specific parabola is written as *y* = 2*x*^2 - 3*x* + 6. This equation is in _____

#### Question 15 15. Each point on the curve of a parabola is _____ to the focus and the directrix.

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Question 16
16.
Given that *F* and *G* are the foci of the hyperbola shown, which of the following statements is true?

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Question 17
17.
Given that *FP* + *GP* is constant for all *P* on the ellipse shown, which of the following statements is true?

#### Question 18 18. Give the definition of a hyperbola in terms of its foci.

#### Question 19 19. Give the definition of an ellipse in terms of its foci.

#### Question 20 20. Which of the following statements is true about an ellipse and/or hyperbola?

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#### Question 21 21. In the standard form of the equation for an ellipse, the center's coordinates are equivalent to:

#### Question 22 22. An ellipse is a shape where the set of all points where the sum of the distances from the foci is:

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Question 23
23.
The equation of an ellipse is where *c*2 = *a*2 - *b*2. What is *a* equal to if the length of the major axis is 6?

#### Question 24 24. If the larger denominator of the standard form of the equation is underneath the y-variable, then the major axis is:

#### Question 25 25. Foci are:

#### OAE Mathematics: Conic Sections 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!