# GACE Math: Conic Sections Chapter Exam

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Question 1
1.
For a parabola given by *y* = 4(*x* - 3)(*x* - 4), the form of this equation is _____

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

#### Question 3 3. Each point on the curve of a parabola is _____ to the focus and the directrix.

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Question 4
4.
When a parabola equation is written as *y* = -5(*x* -2)^2 + 6, the form is _____

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

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#### Question 6 6. How do we define a parabola using its focus and directrix?

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Question 7
7.
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 8
8.
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*?

#### Question 9 9. What do we call the highest or lowest point of a parabola?

#### Question 10 10. What is the shape of a parabola?

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Question 11
11.
Given that *FP* + *GP* is constant for all *P* on the ellipse shown, which of the following statements is true?

#### Question 12 12. Which of the following statements is true about an ellipse and/or hyperbola?

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Question 13
13.
Given that *F* and *G* are the foci of the hyperbola shown, which of the following statements is true?

#### Question 14 14. Give the definition of a hyperbola in terms of its foci.

#### Question 15 15. Give the definition of an ellipse in terms of its foci.

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#### Question 16 16. If the larger denominator of the standard form of the equation is underneath the y-variable, then the major axis is:

#### Question 17 17. An ellipse is a shape where the set of all points where the sum of the distances from the foci is:

#### Question 18 18. Foci are:

#### Question 19 19. In the standard form of the equation for an ellipse, the center's coordinates are equivalent to:

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Question 20
20.
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?

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#### Question 21 21. Which of the following is the shape of a hyperbola?

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Question 22
22.
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*?

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Question 23
23.
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 24 24. What is the definition of a hyperbola?

#### Question 25 25. 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?

#### GACE Math: 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!