What are the co-vertices of the following graph?

The co-vertices are (1 , 4) , (1 , 0)

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1  ,Where

# The length of the transverse axis is 2a

# The coordinates of the vertices are (h ± a , k)

# The length of the conjugate axis is 2b

# The coordinates of the co-vertices are (h , k ± b)

# The coordinates of the foci are (h ± c , k), where c² = a² + b²

* Lets solve the problem

- From the graph

∵ The vertices of the hyperbola are (6 , 2) and (-4 , 2)

∵ The length of the transverse axis is 2a

- The length of the transverse axis is the difference

  between the x-coordinates of the vertices

∴ The length of the transverse axis = 6 - (-4) = 6 + 4 = 10

∴ 2a = 10 ⇒ divide both sides by 2

∴ a = 5

∵ The coordinates of the vertices are (h + a , k) and (h - a , k)

∵ The vertices of the hyperbola are (6 , 2) and (-4 , 2)

∴ k = 2

∴ h + a = 6 and h - a = -4

∵ a = 5

∴ h + 5 = 6 ⇒ subtract 5 from both sides

∴ h = 1

∴ The center of the hyperbola is (1 , 2)

∵ The length of the conjugate axis is 2b

- The length of the conjugate axis is the difference

  between the y-coordinates of the co-vertices

∴ The length of the conjugate axis = 4 - 0 = 4

∴ 2b = 4 ⇒ divide both sides by 2

∴ b = 2

∵ The coordinates of the co-vertices are (h , k + b) and (h , k - b)

∵ h = 1 , k = 2 , b = 2

∴ The co-vertices are (1 , 2 + 2) and (1 , 2 - 2)

∴ The co-vertices are (1 , 4) , (1 , 0)

2 1/2 feet

step-by-step explanation: