How to solve this analytic geometry problem completely


I want to find a plane that passes through points {1,0,0} and {0,1,0} and is tangent to surface $ z(x,y)=x^{2}+y^{2}$ .

Solve[{a, b, c}.{1, 0, 0} == d && a*0 + b*1 + c*0 == d &&    a*x0 + b*y0 + c*z0 == d && z0 == x0^2 + y0^2 &&    VectorAngle[{a, b, c}, {-2 x0, -2 y0, 1}] ==     0,(*MatrixRank[{2x0,2y0,1},{a,b,c}]\[Equal]1*){a, b, c, d, x0, y0,    z0}] 

But I can’t get the answer I want with the above code(the answer is $ z=0$ and $ 2x+2y-z=2$ ). What should I do?