If the plane 3(x−2)+(y−2)+6(z+3)=0 contains the line x−2a=y−2b=z+31 whose inclination with X-axis is 600, then it satisfies the equation

The d.r’s of line are a,b,1 ∴The d.c.’s of line are aa2+b2+1,ba2+b2+1,1a2+b2+1∴cos600=aa2+b2+1⇒12=aa2+b2+1 i.e.2a=a2+b2+1, i.e.,3a2=b2+1  ............(1)As the plane contains the given line, we have  3(a)+1(b)+6(1)=0................(2)Eliminating b from (1) & (2), we get 3a2=−(6+3a)2+1i.e.6a2+36a+37=0,