Write a conic section with polar equation the focus at the origin and the given data hyperbola, eccentricity 2.5, directrix y = 2

Anish Buchanan 2020-11-06 Answered
Write a conic section with polar equation the focus at the origin and the given data hyperbola, eccentricity 2.5, directrix y = 2

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Expert Answer

Obiajulu
Answered 2020-11-07 Author has 15070 answers
Step 1 Given: Focus (0, 0) Eccentricity \(= e =2.5\) Directrix = d = 2 The formula for polar equation of any conic sections, when the focus is at origin \(r(\theta) = \frac{ed}{1+e cos(\theta - \theta_0)}\) Step 2 Since \(y=d\), the formula becomes \(r(\theta) = \frac{ed}{1+e sin \theta}\)
\(r(\theta) = {2.2\times2}{1+2.5 sin \theta}\)
\(= \frac{10}{2=5 sin \theta}\)
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