A lemniscate is a figure-eight shaped curve with the equation:
$(x^2 + y^2)^2 = 2a^2(x^2 - y^2)$
Now, we are given two points on the lemniscate: (1, 2) and (2, 1). We can plug these points into the equation to find the value of $a^2$.
For point (1, 2):
$(1^2 +
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