3.1.12 Curves of the 2-nd order

Problem: Reduce the equation of the second-order curve \( f(x, y)=0 \) to canonical form and find its points of intersection with the straight line \( A x+B y+C=0 \). \( 2 x^{2}+4 x+y^{2}-2=0, \quad 2 x+y-2=0 \).