Projective Variety of a Quadric is Tangent to x=0

Question

I'm trying to find a quadric $f$ such that the projective variety of $f$ is tangent to the lines $x=0, y=0$, and $z=0$. I then need to parametrize the affine piece and the piece at infinity.

I'm not really sure at all where to start in even finding the quadric.

Answer 1

$$f(x,y,z)=x^2+y^2+z^2-2xy-2yz-2xz$$