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Question

The equation of the directrices of the hyperbola 3x23y218x+12y+2=0 is 
  1. x=3±136
  2. x=6±313 
  3. x=3±613
  4. x=6±133 


Solution

The correct option is A x=3±136
3x23y218x+12y+2=0
3(x26x)3(y24y)+2=0
 3(x3)23(y2)2=2+2712
 (x3)2(y2)2=133
(x3)2(13/3)2(y3)2(13/3)2=1

Equation of directrix are xk=±ae
x3=±13/313/3+13/3x=3±136 

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