Hyperbola
Directrices
Premium Question
Grade 11
Question:
The directrices of the hyperbola $\frac{(x - 1)^2}{9} - \frac{(y - 2)^2}{4} = 1$ are:
(1) $x = 1 \pm \frac{9}{\sqrt{13}}$
(2) $x = \pm \frac{9}{\sqrt{13}}$
(3) $x - 1 = \pm \frac{3}{\sqrt{13}}$
(4) $x = 1 \pm \frac{3}{\sqrt{13}}$
Step-by-Step Solution
Key Concept: Centre $(1, 2)$, $a^2 = 9$, $b^2 = 4$, $c = \sqrt{13}$, $e = \sqrt{13}/3$. Directrices: $x - 1 = \pm a/e = \pm 9/\sqrt{13}$, so $x = 1 \pm 9/\sqrt{13}$.
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Correct Answer: (1)