An equation of the form ax2 + bx + cy2 + dy + e = 0 where aa and cc have opposite signs might represent a
hyperbola.
a. apply the process of completing the square in both xx and yy to convert the equation
9x2 − 36x − 4y2 − 8y − 4 = 0 to one of the standard forms for a hyperbola: (x−h)2 / a2 − (y−k)2 / b2 = 1 or (y−k)2 / b2 − (x−h)2 / a2 = 1.
b. find the center of this hyperbola.
c. find the asymptotes of this hyperbola.
d. graph the hyperbola