No, the acceleration due to change in direction is not the same for both the bodies in this scenario.
Let's consider the body moving along a circle first. In uniform circular motion, the velocity of the body is always tangent to the circle, and its magnitude remains constant. However, since the direction of the velocity is continuously changing, the body experiences acceleration towards the center of the circle. This acceleration is called centripetal acceleration and is directed radially inward.
On the other hand, in the case of the body moving along an ellipse, the situation is different. In general, an ellipse does not have a constant curvature. This means that the radius of curvature, and therefore the direction of the velocity, changes as the body moves along the ellipse. As a result, the acceleration is not constant along the ellipse. It varies depending on the position of the body on the ellipse.
In an ellipse, the acceleration is not directed purely towards the center like in a circle. Instead, it has two components: tangential acceleration and normal acceleration. The tangential acceleration is responsible for changing the speed of the body along the ellipse, while the normal acceleration is responsible for changing its direction. Since the ellipse has varying curvature, the magnitude and direction of these components of acceleration change as the body moves along the ellipse.
In conclusion, the acceleration due to change in direction is not the same for both the bodies. The body moving along the circle experiences a constant centripetal acceleration, while the body moving along the ellipse experiences varying tangential and normal accelerations, which are not uniform along the ellipse.