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A unit circle is placed at the origin. At any point along the circle we can draw a tangent line and calculate its slope. Then we can plot (x-coordinate, slope). It seems to make this nice curved X shape. Can we make an equation for it?**

Your task is to find an equation, without trigonometry.

Note: As interesting as it was to try drawing the shape on a whiteboard, I had to fight the urge to use trig for this equation. In fact, I think it has a nice parametric form using trig, so you could also find that. Or whatever you like. We were just playing around with some math.