Actually, that's what the offset of the curve looks like. Take a pencil and paper and draw a parabola. Then try to draw an offset curve to the inside with an of

Actually, that's what the offset of the curve looks like. Take a pencil and paper and draw a parabola. Then try to draw an offset curve to the inside with an offset greater than the smallest curvature radius of the parabel. You will get this strange path with two cusps and an inverted curve between them. Try it out, it is an eye opener.