For a hyperbola  [tex]\dfrac{y^{2}}{a^{2}}-\dfrac{x^{2}}{b^{2}}=1[/tex]
where  [tex]a^{2}+b^{2}=c^{2}[/tex]
the directrix is the line  [tex]y=\dfrac{a^{2}}{c}[/tex]
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.
