text: #### Find the equation of the hyperbola whose directrix is 2x + y = 1, focus (1, 2) and eccentricity   Option 1) 7x2 - 2y2 + 12xy - 2x + 14y - 22 = 0 Option 2) 7x2 - 2y2 + 2xy - 2x + 14y - 22 = 0 Option 3) 7x2 - 2y2 + xy - 14x + 2y - 22 = 0 Option 4) none of the above
  
  Eccentricity -
  
  The ratio of a distance of point from focus to distance from fixed line.
  
  - wherein
  
  It is donated by .
  
  &
  
  Directrix -
  
  The fixed straight line of a conic section.
  
  - wherein
  
  &
  
  Focus -
  
  The fixed point of a conic section
  
  - wherein
  
  Option 1)
  
  7x2 - 2y2 + 12xy - 2x + 14y - 22 = 0
  
  This solution is correct
  
  Option 2)
  
  7x2 - 2y2 + 2xy - 2x + 14y - 22 = 0
  
  This solution is incorrect
  
  Option 3)
  
  7x2 - 2y2 + xy - 14x + 2y - 22 = 0
  
  This solution is incorrect
  
  Option 4)
  
  none of the above
  
  This solution is incorrect