Given the information below, write the equation in Standard Form.

Hyperbola:

Vertices (-4, 5), (4, 5)
Foci (-6, 5), (6, 5)

The standard form of the equation of a hyperbola is  

Step-by-step explanation:

The standard form of the equation of a hyperbola with center (h , k) is   , where

∵ The vertices of the hyperbola are (-4 , 5) and (4 , 5)

∴ k = 5

∴ h + a = 4 ⇒ (1)

∴ h - a = -4 ⇒ (2)

- Add (1) and (2)

∴ 2h = 0

- Divide both sides by 2

∴ h = 0

- Substitute the value of h in (1) or (2) to find a

∵ 0 + a = 4

∴ a = 4

∵ The foci of the hyperbola are (-6 , 5) and (6 , 5)

∴ k = 5

∴ h + c = 6 ⇒ (1)

∴ h - c = -6 ⇒ (2)

- Add (1) and (2)

∴ 2h = 0

- Divide both sides by 2

∴ h = 0

- Substitute the value of h in (1) or (2) to find c

∵ 0 + c = 6

∴ c = 6

Let us use the rule c² = a² + b²

∵ (6)² = (4)² + b²

∴ 36 = 16 + b²

- Subtract 16 from both sides

∴ 20 = b²

∵ The standard form of the equation of a hyperbola is  

- Substitute the values of h, k, a and b in the equation

∴

∴

The standard form of the equation of a hyperbola is  

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the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0