If $5x + 9 = 0$ is the directrix of the hyperbola $16x^2 - 9y^2 = 144$, then the corresponding focus is:
Step-by-Step Solution
Key Concept: Hyperbola: $x^2/9 - y^2/16 = 1; a^2 = 9, b^2 = 16, c = 5$. Directrix $x = -a^2/c = -9/5$ (nearer to left focus $(-5, 0)$). The given directrix $5x + 9 = 0 \Rightarrow x = -9/5$, so corresponding focus is $(-5, 0)$.
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Correct Answer: (1)