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A circle is drawn with its centre at one focus of the hyperbola x²/9 - y²/16 = 1, such that the circle is internally tangent to the hyperbola with no part of the circle lying outside (beyond) the curve. Find the radius of this circle.
- less than 2
- equal to 2
- 11/3
- none of these
Correct answer: less than 2
Solution
With a = 3, b = 4, c = 5, the focus is at (5,0). The closest the curve comes (and the largest fully-contained circle) gives a radius strictly less than c - a = 2.
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