that has the following characteristics:

At t=0, the curve starts at the point (-4,4), travels to (3,-1) along an interesting non linear path, and returns to (-4,4) along a curved path that is a reflection of the path from (-4,4) to (3,-1) across the line through (-4,4) and (3,-1). Describe briefly how you can systematically come up with such a curve( in other words, what properties of parametric equations can you use to come up with such a curve if you were given different points)?