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

question 66

Multiple Choice

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

• 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 \( \left(\frac{1}{2}, 0\right),\left(-\frac{3}{2}, \pi\right) \)

---

Definitions:

Psychological Traits

Enduring characteristics of an individual's behavior, thought, and emotion, which demonstrate a degree of consistency over time.

Physical Activities

Any form of exercise or movement of the body that uses energy, ranging from brisk walking to competitive sports.

Historical Racism

Discrimination or prejudice against people based on their race rooted in history, impacting social and institutional structures over time.

African Americans

A racial or ethnic group in the United States with ancestors from any of the black racial groups of Africa.