Answer:
The answer to your question is [tex]\frac{x^{2}}{16} - \frac{y^{2} }{25} = 1[/tex]
Step-by-step explanation:
Data
(-4, 0) (4, 0)
(0, 5) (0, -5)
Plot the point to determine if it is a horizontal or vertical hyperbola
It is a horizontal hyperbola because the vertices are in a horizontal line. The center is (0, 0).
a = 4
b = 5
Formula
[tex]\frac{x^{2} }{a^{2}} - \frac{y^{2}}{b^{2}} = 1[/tex]
Substitution
[tex]\frac{x^{2}}{4^{2}} - \frac{y^{2}}{5^{2}} = 1[/tex]
Equation
[tex]\frac{x^{2}}{16} - \frac{y^{2}}{25} = 1[/tex]
