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Tangent Curves

Y=alpha*x^2 + alpha*x + (1/24)

x=alpha*y^2 + alpha*y + (1/24)

These are two curves.
For what values of alpha are these two curves tangent to each other.

Solution Summary

Values are found to make two curves tangent to each other. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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