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How to Draw the Famous Batman Curve


The ellipse \displaystyle \left( \frac{x}{7} \right)^{2} + \left( \frac{y}{3} \right)^{2} - 1 = 0 looks like this:

ellipse

So the curve \left( \frac{x}{7} \right)^{2}\sqrt{\frac{\left| \left| x \right|-3 \right|}{\left| x \right|-3}} + \left( \frac{y}{3} \right)^{2}\sqrt{\frac{\left| y+3\frac{\sqrt{33}}{7} \right|}{y+3\frac{\sqrt{33}}{7}}} - 1 = 0 is the above ellipse, in the region where |x|>3 and y > -3\sqrt{33}/7:

ellipse cut

That’s the first factor.
(more…)

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