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.

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.

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.
