There is a hyperbola in blue with two vertices highlighted at (2,-3) and (-8,-3). It's center is at (-3,-3) highlighted by orange and its Foci is also hightlighted in lightgreen at ($-3-5\sqrt{2}$,-3) and ($-3+5\sqrt{2}$,-3). 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 (2,-3) and (-8,-3). It's center is at (-3,-3) highlighted by orange and its Foci is also hightlighted in lightgreen at ($-3-5\sqrt{2}$,-3) and ($-3+5\sqrt{2}$,-3). 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 (2,-3) and (-8,-3). It's center is at (-3,-3) highlighted by orange and its Foci is also hightlighted in lightgreen at ($-3-5\sqrt{2}$,-3) and ($-3+5\sqrt{2}$,-3). Find the equation of the hyperbola.
