It's more complicated than you might think...

The formula for the length of part (L) of a curve is

The equation of an oval, more correctly called an ellipse, is

Rearranging gives

This becomes difficult to work with as an ellipse is not the graph of a function. If one point is below the x-axis and the other above then you have to use both square roots separately, because an ellipse is the joint graph of those two square roots above...