how to calculate the radius of a circle which is drawn below(inwards) the hyperbola curve touching it.need a relationship between these hyperbola and circle .If a circular object is place below the hyperbola touching it how to calculate the radius of the circular object.
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In what form is the hyperbola? If is pole is at $0$ and its abscissa ($\lim_{x\to\infty} f(x)$) is $0$ you need to find a point where $\pmatrix{1\f'(x)}$ is orthogonal to $\pmatrix{x\f(x)}$. This point will be on the circle and the center will be $\pmatrix{0\0}$. – AlexR Oct 09 '14 at 06:35