3.1.43 Curves of the 2 -nd Order

Condition: bring the equations of lines of the 2nd order to the canonical appearance, build these lines (indicate the "old" and "new" coordinate systems in the drawing). a) \ (y^{2} +6 x+8 y+40 = 0 \) \ (x^{2}+y^{2} +6 x+2 y-6 = 0 \) c) \ (16 x^{2} -1 y^{2} +128 x-2 y+239 = 0 \) \ (4 x^{2}+y^{2} -24 x+8 y+48 = 0 \).