Write an equation for the hyperbola. It's center is (0,0).
Foci:(-4,0), (4,0)
vertices:(-3,0), (3,0)
To write the equation of the hyperbola with the given information, we will use the standard form for a hyperbola centered at the origin.
In the standard form, the equation of a hyperbola with a horizontal transverse axis is:
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
where (h, k) represents the center of the hyperbola, a is the distance from the center to each vertex or each focus, and b is the distance from the center to each co-vertex or each point on the conjugate axis.
In this case, the center of the hyperbola is (0,0), which gives us h = 0 and k = 0.
The distance from the center to each focus is given as 4, so a = 4.
The distance from the center to each vertex is given as 3, so b = 3.
Plugging these values into the standard form equation, we get:
(x - 0)^2 / 4^2 - (y - 0)^2 / 3^2 = 1
Simplifying, we have:
x^2 / 16 - y^2 / 9 = 1
So, the equation of the hyperbola is:
x^2 / 16 - y^2 / 9 = 1