Problem

11. Find the directrix for the polar equation \( r=\frac{8}{2-6 \sin \theta} \).

Answer

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Answer

3. Calculate directrix: \(D = \dfrac{2}{6} = \dfrac{1}{3}\)

Steps

Step 1 :1. Identify the conic form: \(r = \dfrac{8}{2 - 6 \sin \theta}\)

Step 2 :2. Rewrite as: \(r(2 - 6 \sin \theta) = 8\)

Step 3 :3. Calculate directrix: \(D = \dfrac{2}{6} = \dfrac{1}{3}\)

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