Hyperbolas Lesson

What is the center of the hyperbola?

• (0, 4)
• (4, 0)
• (-4, 0)
• (0, -4)

Is the hyperbola vertical or horizontal? 

• Vertical
• Horizontal

What are the vertices of the hyperbola?

• (0, 5) and (0, -5)
• (5, 0) and (-5, 0)
• (0, 25) and (-25, 0)
• (0, 0) and (0, 5)

A hyperbola with a horizontal tranverse axis has asymptotes y = ± ¾x.  Which of the following could be the equation of the hyperbola in standard form.

• x²/3 + y²/4 = 1
• x²/4 - y²/3 = 1
• x²/16 - y²/9 = 1
• x²/25 - y²/16 = 1

What are the foci of the hyperbola with the equation y²/12 - x²/5 = 1

• (0, ±√17)
• (±√17, 0)
• (0, ±√7)
• (±√7, 0)

What are the asymptotes of the hyperbola in the picture?

• y = x and y = –x
• y = 2x and y = –2x
• y = ¹/₂x and y = –¹/₂x
• y = 2x and y = 4x

Write the standard form of the following equation:
x² - 4y² + 6x - 8y = 11

• A
• B
• C
• D

Write the standard form of the following equation:
9y² - 4x² + 36y + 32x - 64 = 0

• A
• B
• C
• D

What is the value of a² for the given hyperbola?

• 1
• -2
• 25
• 16

What is the equation describing the relationship between dimensions and foci of a hyperbola?

• c² = a² + b²
• c² = a² - b²
• 4p
• (x-h)² + (y-k)² = r²