one-parameter family of conics
Hi to everybody!!!!
I have to find a solution to these problems, but i'm not able.
The question are:
1.What is the general formula for the one parameter family of conics through the points (1,1), (1,-1), (-1,-1), (-1,1).
I hope someone can help me! Thank you very much.
2. Suppose R=[u] and S=[s] are two points in the projective space neither lying an a given conic defined by the symmetric bilinear form B. Show that RS is tangent to the conic if and only if B(u,u)B(v,v)-(B(u,v))^2=0.