Hyperbolas

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

Tags

CCSS.HSG.CO.C.10

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

• (0, ±√13)

• (±√13, 0)

• (0, ±√7)

• (±√7, 0)

Is the hyperbola vertical or horizontal? 

• Vertical
• Horizontal

What are the vertices of the hyperbola?

• (0, 3) and (0, -3)
• (-4, 3) and (-4, -3)
• (0, 1) and (0, -1)
• (4, 0) and (-4, 0)

A hyperbola has vertices (±5, 0) and one focus at (6, 0). What is the equation of the hyperbola in standard form?

• x²/25 + y²/11 = 1
• x²/5 - y²/11 = 1
• x²/11- y²/25 = 1
• x²/25 - y²/11= 1

Written in standard form, this would be . . .

• A

• B

• C

• D

A hyperbola centered at (-3, 2) with a horizontal tranverse axis has asymptotes y = ± ¾x.  Which of the following could be the equation of the hyperbola in standard form?

• (x + 3)²/16 + (y - 2)²/ 9 = 1
• (x + 3)²/ 4 - (y - 2)²/ 3 = 1
• (x + 3)²/16 - (y - 2)²/ 9 = 1
• (x + 3)²/ 9 - (y - 2)²/ 16 = 1

The vertices of a hyperbola are located at (1,1) and (5 ,1). Which are the coordinates of the center?

• (3,1)

• (3,0)

• (1,3)

• (9,1)

What is the value of a² for the given hyperbola?

• 1
• 5
• 25
• 16

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