Find the equation of the hyperbola with:
(a) Foci (1, −3) and (1, 5) and one vertex (1, −1).
(b) Vertices (2, −1) and (2, 3), and asymptote x = 2y.
Consider the set of points described by the equation 16x2 −4y2−64x−24y+19=0.
(a) Show that the given equation describes a hyperbola and findthe center of the hyperbola.
(b) Determine the equations of the directrices as well as theeccentricity.
