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

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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Obiajulu
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 $$r(\theta) = \frac{ed}{1+e sin \theta}$$
$$r(\theta) = {2.2\times2}{1+2.5 sin \theta}$$
$$= \frac{10}{2=5 sin \theta}$$