An osculating circle Find the values of h, k, and a that

Chapter 3, Problem 5AAE

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Problem 5AAE

An osculating circle Find the values of h, k, and a that make the circle (x h)2 + ( y k)2 = a2 tangent to the parabola at the point (1, 2) and that also make the second derivatives d2y/dx2have the same value on both curves there. Circles like this one that are tangent to a curve and have the same second derivative as the curve at the point of tangency are called osculating circles (from the Latin osculari, meaning “to kiss”). We encounter them again in Chapter 13.

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