HyperbolaHardBloom L3
Question
With one focus of the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$ as the centre, a circle is drawn which is tangent to the hyperbola with no part of the circle being outside the hyperbola. The radius of the circle is:
Options
A.less than 2
B.2
C.$\frac{11}{3}$
D.none of these
Solution
Sol. (b)
$$\begin{matrix} 16 & \ = 9\left( e^{2} - 1 \right) \\ e & \ = \frac{5}{3} \\ F_{1} & \ = (5,0) \end{matrix}$$
Circle can be drawn touching hyperbola at point $A$ or $B$ only
$\therefore\ $ Radius $= 2$
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