question: There is a hyperbola in blue with double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. 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 double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. 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 double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. Find the equation of the hyperbola.
  
question_for_eval: There is a hyperbola in blue with double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. Find the equation of the hyperbola.
  