Final answer:
To express the given hyperbola equation (25x²-16y²=400) in standard form, divide each term by 400 resulting in x²/16 - y²/25 = 1, which is the standard form of the equation.
Step-by-step explanation:
To write the hyperbola equation 25x²-16y²=400 in standard form, we need to divide every term by the constant on the right side of the equation, which in this case is 400. Doing this, we get ¼ x² - ¼ y² = 1. This represents a hyperbola in standard form where the difference of the squares is equal to 1, which can be written as:
x²/a² - y²/b² = 1
Comparing this with the equation we derived earlier, we find a² = 16 and b² = 25. Therefore, the standard form of the hyperbola is:
x²/16 - y²/25 = 1