A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation of the hyperbola?
To find the standard form of a hyperbola with vertices and a focus given, we can use the formula:
c^2 = a^2 + b^2
Where a is the distance from the center to the vertex, b is the distance from the center to the co-vertex, and c is the distance from the center to the focus.
In this case, the distance from the center to the vertex is 5, and the distance from the center to the focus is 6. The value of c is given as 6.
Using the formula, we can calculate b:
6^2 = 5^2 + b^2
b^2 = 36 - 25
b^2 = 11
b = √11
Therefore, the equation of the hyperbola in standard form is:
(x^2/25) - (y^2/11) = 1