Equation of hyperbola:
Eccentricity:
Foci:
Equation of directrices:
You have to solve from this.
Here comes a slightly different approach:
1. Let P denotes an arbitrary point on the hyperbola, r the distance of P to the focus F and l the distance of P to the directrix. Then
2. Plug in the values you know:
3. Simplify and re-arrange so that you'll get the equation of the hyperbola in standard form. I've got: