The equation of a common tangent with positive slope to the circle $x^2 + y^2 - 8x = 0$ and the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$ is:
Step-by-Step Solution
Key Concept: Tangent to hyperbola: $y = mx + c$ with $c^2 = 9m^2 - 4$. Distance from centre $(4, 0)$ of circle to tangent $= 4$: $\frac{|4m - c|}{\sqrt{1 + m^2}} = 4$. Also $c^2 = 9m^2 - 4$. Solve with positive $m$ to get $m = 2/\sqrt{5}$, $c = -4/\sqrt{5}$, i.e., $2x - \sqrt{5} y + 4 = 0$.
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Correct Answer: (2)