Refer to the diagram shown below.
The vertex is at (a,0), with a = 5.
The focus is at (c,0), with c = 9.
Therefore
b² = c² - a² = 81 - 25 = 56
The equation of the hyperbola is
[tex] \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} =1, \\ or \\ \frac{x^{2}}{25} - \frac{y^{2}}{56}=1 [/tex]
Answer:
[tex] \frac{x^{2}}{25} - \frac{y^{2}}{56} =1[/tex]
