The equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
How to determine the equation of the hyperbola?
The vertices of the hyperbola are given as:
Vertices = (±4, 1)
The foci of the hyperbola are given as:
Foci = (±5, 1)
The coordinates of the vertices is represented as::
Vertices = (±a, n)
By comparing (±a, n) and (±4, 1), we have:
a = 4
n = 1
The coordinates of the foci is represented as::
Foci = (±c, n)
By comparing (±c, n) and (±5, n), we have:
c = 5
n = 1
Calculate b using:
b = √(c² - a²)
So, we have:
b = √(5² - 4²)
Evaluate
b = 3
The equation of a hyperbola is:
[tex]\frac{x^2}{a^2} - \frac{(y - n)^2}{b^2} = 1[/tex]
So, we have:
[tex]\frac{x^2}{4^2} - \frac{(y - 1)^2}{3^2} = 1[/tex]
Evaluate the exponent
[tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
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