Answer:
1:2 - one dog to two cats.
If it's a square all sides are 9 feet...9x9=81
With

we have

The vector field evaluated over this parameterization is

so the line integral is


A circle with center
and radius
has equation

If we substitute
in this equation, we have

This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:

The expression simplifies to

The solutions to the associated equation are

So, the parabola is negative between the two solutions:
