Discuss the Equation and Graph It $$r = \frac { 3 } { 2 + 4 \sin \theta }$$

question 55

Multiple Choice

Discuss the equation and graph it.
- $$r = \frac { 3 } { 2 + 4 \sin \theta }$$

• A) ellipse, directrix parallel to the polar axis \( \frac{3}{2} \) unit below the pole vertices \( \left(\frac{3}{2}, \frac{\pi}{2}\right),\left(\frac{1}{2}, \frac{3 \pi}{2}\right) \)
• B) ellipse, directrix perpendicular to the polar axis \( \frac{3}{2} \) unit left of the pole vertices \( \left(\frac{3}{2}, 0\right),\left(\frac{1}{2}, \pi\right) \)
• C) hyperbola; directrix parallel to the polar axis \( \frac{3}{4} \) unit above the pole vertices \( \left(\frac{1}{2}, \frac{\pi}{2}\right),\left(-\frac{3}{2}, \frac{3 \pi}{2}\right) \)
• D) hyperbola, directrix perpendicular to the polar axis \( \frac{3}{4} \) unit right of the pole vertices \( \left(\frac{1}{2}, 0\right),\left(-\frac{3}{2}, \pi\right) \)

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