What is the distance between the two foci of the hyperbola 25x^{2}-75y^{2}=225?
- A. 2\sqrt{3} units
- B. 4\sqrt{3} units ✓
- C. \sqrt{6} units
- D. 2\sqrt{6} units
Correct Answer: B. 4\sqrt{3} units
Explanation
Divide by 225 to get the standard form: \frac{x^2}{9} - \frac{y^2}{3} = 1. Here a^2=9 and b^2=3. Using b^2 = a^2(e^2-1), we get 3 = 9(e^2-1) \implies e^2 = 4/3 \implies e = 2/\sqrt{3}. The distance between the foci is 2ae = 2(3)(2/\sqrt{3}) = 4\sqrt{3}.
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