question: There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\sqrt{2}$) and (-1, -$3\sqrt{2}$). Find the equation of the hyperbola.
  
query_wo: Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
  Question: There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\sqrt{2}$) and (-1, -$3\sqrt{2}$). Find the equation of the hyperbola.
  
query_cot: Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
  Question: There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\sqrt{2}$) and (-1, -$3\sqrt{2}$). Find the equation of the hyperbola.
  
question_for_eval: There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\sqrt{2}$) and (-1, -$3\sqrt{2}$). Find the equation of the hyperbola.
  