Answer:
The answer to your question is
[tex]\frac{(x - 2)^{2} }{4} - \frac{(y - 1)^{2}}{5} = 1[/tex]
Step-by-step explanation:
Data
Foci (-1, 1) and (5, 1) [A and B]
Vertices (0, 1) and (4, 1) [C and D]
See the image below. From the image we can conclude that it is a horizontal hyperbola.
Equation
[tex]\frac{(x - h)^{2} }{a^{2} } - \frac{(y - k)^{2} }{b^{2} } = 1[/tex]
From the image calculate the center
The center is in the middle of the vertices (2, 1)
Now, calculate a, a is the distance from the center to the vertices, a = 2
Calculate c, c is the distance from the center to the foci, c = 3
Calculate b with the pythagorean theorem c² = a² + b²
b² = c² - a²
b² = 3² - 2²
b² = 9 - 4
b² = 5
Substitution
[tex]\frac{(x - 2)^{2} }{4} - \frac{(y - 1)^{2}}{5} = 1[/tex]
