The center of a hyperbola is located at (0, 0). one focus is located at (0, 5) and its associated directrix is represented by the line y = 9/5 . given the standard form of the equation of a hyperbola, what are the values of a and b y^2/a^2 + x^2/b^2 = 1 a= b=

For a hyperbola  
where  
the directrix is the line  
and the focus is at (0, c).

Here, we have c = 5, a² = 9, so b² = 5² - 9 = 16.
  a = √9 = 3
  b = √16 = 4

Your hyperbola's constants are ...
  a = 3
  b = 4

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Please note that the equation of a hyperbola has a negative sign for one of the terms. The equation given in your problem statement is that of an ellipse.