3.1.11 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 \( \ell: A x+B y+C=0 \). \( 2 x^{2}+y^{2}-12 x+10=0 \), (e) \( x+y-2=0 \).