Question 385710
The equation represents a hyperbola.  The center is at (0,0).  Here {{{a^2 = 9}}},{{{b^2 = 36}}}, {{{b^2 = c^2 - a^2}}}, or {{{c^2 = a^2 + b^2 = 9+36 = 45}}}.  Hence the foci are ({{{-3sqrt(5)}}}, 0) and ({{{3sqrt(5)}}}, 0). Vertices are (-3,0) and (3,0).  We can get the asymptotes by considering {{{ x^2/9 = y^2/36}}}.  This equation is equivalent to the equations y = -2x and y = 2x, and are the asymptotes of the hyperbola.