Question

1.9. Let C1 and O2 be the cubics given by the following equations (a) Find the nine points of intersection of C1 and C2 (b) Let ((0,0 , P1,.., Psy be the nine points from (a). Prove directly that if a cu- bic curve goes through P,.. . , Ps, then it must go through the ninth point (0, 0). (Do not simply quote the theorem in Section 1.2. This exercise is asking you to prove that theorem for particular curves Ci and C2.)

Answer 1

ANSWER:

Given that

Let  $_{C_1}$ and  $_{C_2}$ be the cubics given by the equations

  $_{C_1}: {x^3}+2{y^3}-x-2y$$= 0$

$_{C_2}:2{x^3}-y^3-2x+y= 0$