# equation of a plane passing through a diameter of a sphere

I want to find the equation of plane passing through a diameter of a sphere, For simplicity let us assume that origin,$(0,0,1)$ and $(0,0,-1)$ are on a diameter, then the points lie on the plane $ax+by+cz=d$ using these points i get $d=0$ and $c=0$, what to do next?

The points $(0,0,1)$, $(0,0,0)$ and $(0,0,-1)$ do not define a plane uniquely. A plane of the form $\{(x,y,z)\in\mathbb{R}^3|ax+by=0\}$ will work for any $a,b\in\mathbb{R}$ not both zero.