Back substitution is to directly substitute the linear equation into the original conic equation; Thus, Vieta's theorem is obtained.

The difference method can give you an example: suppose it is an elliptic equation: x 2/a 2+y 2/b 2 =1; The straight line ax+by+c = 0; The two intersections are (x 1, y1); (x2，y2)；

Therefore, x12/a 2+y12/b 2 =1.

x2^2/a^2+y2^2/b^2= 1

Subtract the two equations to get (x1-x2) (x1+x2)/a2+(y1-y2) (y 21+y2)/b2 = 0;

ax 1+by 1+c = 0；

ax2+by2+c = 0；

So we can get a series of expressions. I hope you can understand;