3.1.43 Curves of the 2nd order

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