Circle Trapped in a Hyperbola

Geometry Level 3

A circle of radius equal to 3 units, gets trapped in the upper half of the plane, between the branches of the hyperbola,

\[ x^2 -\dfrac{y^2}4 = 1. \]

Which of the following is the best estimate for the \(x\)-coordinate of the point of tangency in the first quadrant?

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