How do you write an equation for the hyperbola with a centre at (-3,1), one focus (-5,1), length of conjugate axis 4?
One cannot have a hyperbola with the equation:
and that is what your specifications imply.
Because the center and the given focus share the same y coordinate, we know that this is a horizontal transverse type with a general equation of the form:
We are given that the center
We are given the length of the conjugate axis is 4; this allows us to find b:
Substitute this into the equation:
We are given that a focus is at
We can find