3.1.31 Curves of the 2 -nd Order

Condition: using the allocation of a full square, bring the equation of a second-order curve \ (9 x^{2} -36 x-16 y^{2} -32 y-124 = 0 \ quad \) to the canonical appearance. Determine the type of curve, find its semi -shafts, eccentricity, coordinates of the peaks and tricks, the equations of the director and asymptot (if available). Make a drawing.