I am having issues with finding hyperbola equations with a translation when it gives the vertices and foci.
vertices: (-5,5) (5,5)
foci: (-7,5) (7,5)
The focal axis is horizontal, so the equation is in the form
The center (h, k) is in between the two vertices, so it's (0, 5).
a is the distance from the center to one of the vertices, so a = 5.
c is the distance from the center to one of the foci, so c = 7.
The relationship between a, b, c is
so solve for b:
So the equation should be
Nothing to it!