If A is a positive number, the parametric curve

(x = t^3 − t

y = A/(1 + t^22)

looks like:

For one value of A, the “self-intersection” of the curve is perpendicular. The picture

looks like:

Find that value of A.

link is available: http://math.rutgers.edu/~pranadav/Workshop6Sp10 question 3

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