A

To find the distance between the points of suspension and the center of oscillation for a compound pendulum, we use the relationship involving the points defined by the lengths associated with the pendulum.
Step 1: The moment of inertia is given by a formula that relates the mass, the distance from the axis of rotation, and the distance to the center of mass.
Step 2: For small oscillations, we refer to the distance which is related to the terms $k$ and $\ell$, where $k$ represents a characteristic length and $\ell$ represents the distance to the center of mass from the point of suspension.
Step 3: The formula for the distance between the points of suspension and the center of oscillation can be expressed as:
$$\frac{k^2 - \ell^2}{2}$$
Therefore, the correct answer is Option A.