How do you write the equation of a hyperbola given foci at (1, 5) and (7, 5) and with vertices at (2, 5) and (6, 5)?
Use the equation of hyperbola and
The foci and the vertices all lie along the horizontal line y=5, so the hyperbola opens left/right. This implies that the x term goes first and the y term is subtracted.
The center is half way between the vertices at (4.5) = (h,k).
The vertices are 2 units from the center, so a=2.
The foci are 3 units from center, so c =3.