Question 1

Which of these statements is NOT TRUE of hyperbolas?

Accepted Answer

The two branches of a hyperbola will always open to the left and to the right.

Answer

Hyperbolas are the collection of all points that are a fixed difference between the two foci.

Answer

The vertices of a hyperbola will never be the same points as the foci of the hyperbola.

Answer

They contain a center located at (h, k).

Question 2

Which of the following refers to the line that passes through the center of the hyperbola and is asymptotic to the branches?

Accepted Answer

Asymptotes

Answer

Directrix

Answer

Transverse axis

Answer

Conjugate axis

Question 3

Which of the following refers to the perpendicular bisector of the transverse axis?

Accepted Answer

Conjugate axis

Answer

Asymptotes

Answer

Directrix

Answer

Transverse axis

Question 4

What are the foci of the hyperbola with equation (y^2 / 12) - (x^2 / 5) = 1?

Accepted Answer

(0, ±√17)

Answer

(0, ±√13)

Answer

(0, ±√19)

Answer

(0, ±√12)

Question 5

Which of the following is the equation of the hyperbola whose asymptotes are y = ±2x and passes through (5/2, 3)?

Accepted Answer

(y^2 / 36) - (x^2 / 9) = 1

Answer

(y^2 / 16) - (x^2 / 4) = 1

Answer

(y^2 / 4) - (x^2 / 9) = 1

Answer

(y^2 / 9) - (x^2 / 4) = 1

Question 6

What is the center of the hyperbola defined by the equation 11x^2 - 25y^2 + 22x + 250y - 889 = 0?

Accepted Answer

(-1, -5)

Answer

(-1, 5)

Answer

(1, 5)

Answer

(1, -5)

Question 7

What are the vertices of the hyperbola defined by 11x^2 - 25y^2 + 22x + 250y - 889 = 0?

Accepted Answer

(-1, -5 ± 3)

Answer

(1, -5 ± 3)

Answer

(-1, -5 ± √3)

Answer

(-1, -2) and (-1, -8)

Question 8

Which of the following is the equation of a hyperbola centered at the origin with foci at (±5, 0) and vertices at (±3, 0)?

Accepted Answer

(x^2 / 9) - (y^2 / 16) = 1

Answer

(x^2 / 9) - (y^2 / 25) = 1

Answer

(x^2 / 16) - (y^2 / 9) = 1

Answer

(x^2 / 25) - (y^2 / 16) = 1

Question 9

What is the length of the transverse axis of the hyperbola (x^2 / 49) - (y^2 / 36) = 1?

Accepted Answer

14

Answer

98

Answer

7

Answer

36

Question 10

Which of the following hyperbolas has asymptotes y = ±(3/4)x?

Accepted Answer

(x^2 / 16) - (y^2 / 9) = 1

Answer

(x^2 / 9) - (y^2 / 16) = 1

Answer

(y^2 / 16) - (x^2 / 9) = 1

Answer

(y^2 / 9) - (x^2 / 16) = 1

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