The correct answer is A.
The equation of a catenary is $y = c cosh \frac{x}{c}$, where $c$ is the length of the chain and $x$ is the horizontal distance from the lowest point of the chain.
The other options are incorrect because they do not represent the equation of a catenary.
Option B is the equation of a hyperbolic sine function.
Option C is the equation of a tangent function.
Option D is the equation of a sine function.