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If the plane 3(x2)+(y2)+6(z+3)=0 contains the line x2a=y2b=z+31 whose inclination with X-axis is 600, then it satisfies the equation

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a
6a2+36a+37=0
b
36a2+37=0
c
36a2+37a+36=0
d
a+3=0

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detailed solution

Correct option is A

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,

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