Final answer:
The question involves the field of physics and fluid dynamics related to the boundary surface of a liquid, focusing on the derivation of a specific equation. It is challenging to provide an exact derivation without further context but typically involves principles like surface tension and fluid geometry related to the Young-Laplace equation.
Step-by-step explanation:
The question pertains to the field of physics, specifically fluid dynamics, where the equation in question represents a form of the boundary surface of a liquid. To show that (x/d²)f(1) + (y²/b²)o(1) = 1, we must understand that this equation is likely derived from the general principles of fluid dynamics and surface tension, possibly involving the Young-Laplace equation, which relates the pressure difference across the interface of a liquid to the surface tension and curvature of that interface. The function f(1) denotes an unknown function evaluated at 1, and its role in conjunction with o(1) (a notation that typically signifies a constant or a term that approaches zero as its argument goes to zero) is to satisfy a physical condition related to the geometry or conservation laws (such as the volume of the fluid).
Unfortunately, without a full understanding of how this specific equation was derived or its complete context, it's difficult to provide a step-by-step explanation for this question. However, by employing the principles of fluid mechanics, one can analyze the physical situation described by the equation and utilize the known theoretical framework such as the Laplace law mentioned above to reach the desired conclusion.