Transistor Circuit DC Analysis
for Id=1mA , K= 8 mA/V², Vt=2V

\$V_{GS} =\sqrt{\dfrac{I_D}{K}}+V_t=\sqrt{\dfrac{1mA}{8mA/V^2}}+2V =2.35~V~~~~~~~~2V=Vt=V_{gs(th)}~~~~\$in datasheets has large tolerance   

Gate input impedance = \$ 500k = R1//R2   .....(1)    \$   

Using KVL:  \$ ~~~~6V=V(R1)+ Vgs +Id*Rs ~~~~,~~~Vgs =V(R2),~~Id*Rs=1V   \$   

\$  Vgs=2.35V= \dfrac{R2*(6-1)V}{(R1+R2)}  .........(2) \$

now re-arranging 

\$\dfrac{R1+R2}{R2}=\dfrac{5V}{2.35V}  ~~~ , ~~~ \dfrac{R1}{500k}=\dfrac{R1+R2}{R2}\$

Two equations and two unknowns solve R1,R2 using above.