Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

Foci (±5, 0), the transverse axis is of length 8.

Here, the foci are on the x-axis.

Therefore, the equation of the hyperbola is of the form $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$.

Since the foci are (±5, 0), c = 5.

Since the length of the transverse axis is 8, 2a = 8 ⇒ a = 4.

We know that $a^{2}+b^{2}=c^{2}$.

$\therefore 4^{2}+b^{2}=5^{2}$

$\Rightarrow b^{2}=25-16=9$

Thus, the equation of the hyperbola is $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$.