a hyperbola has vertices (+-5,0) and one focus (6,0) what is the standard form equation of the hyperbol
The standard form equation of a hyperbola with vertices at (+-5,0) and one focus at (6,0) can be written as:
[(x-h)^2 / a^2] - [(y-k)^2 / b^2] = 1
Since the foci and vertices lie on the x-axis, the hyperbola's equation is horizontal. Therefore, the coordinates of the center (h, k) will be at the midpoint between the vertices: (0, 0).
The distance from the center to the vertex is the value of 'a', which is 5.
The distance from the center to the focus is the value of 'c', which is 6.
We can then find the value of 'b' using the formula c^2 = a^2 + b^2.
Using the values we have:
36 = 25 + b^2
b^2 = 11
b = sqrt(11)
Therefore, the standard form equation of the hyperbola is:
[(x-0)^2 / 25] - [(y-0)^2 / 11] = 1
This simplifies to:
x^2 / 25 - y^2 / 11 = 1
The standard form equation of the hyperbola is x^2 / 25 - y^2 / 11 = 1.