The equation of the hyperbola is .
Assume the origin lies at the center of the hyperbola.
\From the equation we know that the hyperbola has a transverse axis that is parallel to the -axis.
Therefore, the foci of the hyperbola is at and
.
Let us assume the parabola opens up, the common focus is at .
The equation of the parabola is .
The focal length of the parabola is given as .
The distance of the parabola is .
Now substiute the value and
in
.
The equation of the parabola is .
The equation of the parabola is .