Given the general quadratic form with 3 variables $(x,y,z)$:
$ax^2 + by^2 +cz^2 + dxy + eyz +fzx + gx + hy + iz = 0$ satisfies $x^2 + y^2 + z^2 = 1$
I would like to ask what is the maximum number of roots of the provided equation. Do you know how to count the number of roots of quadratic form with n variables?
Thanks in advance