Final answer:
The equation of the hyperbola in standard form is (x-7)²/16 - (y-0)²/9 = 1.
Step-by-step explanation:
The equation of the hyperbola in standard form can be determined using the formula (x-h)²/a² - (y-k)²/b² = 1, where (h, k) represents the center of the hyperbola.
In this case, the center of the hyperbola is (7, 0), so we can start by substituting h = 7 and k = 0 into the formula:
(x-7)²/a² - (y-0)²/b² = 1
Next, we need to determine the values of a and b. The distance between the center and the vertex is a, and the distance between the center and the focus is c. In this case, the vertex is at (7, 4) and the focus is at (7, 5), so a = 4 and c = 5.
Using the relationship a² + b² = c², we can solve for b:
4² + b² = 5²
Simplifying the equation:
16 + b² = 25
b² = 9
b = 3
Substituting the values of a and b into the equation:
(x-7)²/4² - (y-0)²/3² = 1
Therefore, the equation of the hyperbola in standard form is (x-7)²/16 - (y-0)²/9 = 1.