How do you write an equation for the hyperbola with center (0,0), vertex (-2,0) and focus (4,0)?
Please see the explanation.
The given, center, vertex, and focus share the same y coordinate, 0, ,therefore, the standard form for the equation of this type of hyperbola is the one corresponding to the Horizontal Transverse Axis type:
Substitute the center
We know that
Observing that the focus is a distance of 4 from the center we set
Substitute 4 for
Solve for b: