Identify the Vertices and the Foci, and Write Equations for the Asymptotes

question 87

Multiple Choice

Identify the vertices and the foci, and write equations for the asymptotes.
- $\frac { 49 x ^ { 2 } } { 36 } - \frac { 49 y ^ { 2 } } { 64 } = 1$

• A) vertices: \(\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)\)
• foci: \(\left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)\)
• asymptotes: \(y = \frac { 3 } { 4 } x\) and \(y = - \frac { 3 } { 4 } x\)
• B) vertices: \(\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)\)
• foci: \(\left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)\)
• asymptotes: \(y = \frac { 4 } { 3 } x\) and \(y = - \frac { 4 } { 3 } x\)
• C) vertices: \(\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)\)
• foci: \(\left( \frac { 70 } { 2,401 } , 0 \right) , \left( - \frac { 70 } { 2,401 } , 0 \right)\)
• asymptotes: \(y = \frac { 4 } { 3 } x\) and \(y = - \frac { 4 } { 3 } x\)
• D) vertices: \(\left( \frac { 7 } { 8 } , 0 \right) , \left( - \frac { 7 } { 8 } , 0 \right)\)
• foci: \(\left. \left( \frac { 10 } { 7 } , 0 \right) , - \frac { 10 } { 7 } , 0 \right)\)
• asymptotes: \(y = \frac { 4 } { 3 } x\) and \(y = - \frac { 4 } { 3 } x\)

---

Definitions:

Supine

A posture in which an individual rests on their back, looking upwards, commonly employed during medical assessments or interventions.

Incentive Spirometer

A device used to help patients improve the functioning of their lungs by encouraging voluntary deep breathing.

Lung Expansion

A respiratory therapy technique aimed at increasing lung volume to improve oxygenation and prevent atelectasis.

Prophylactic Antibiotic

Antibiotics taken to prevent infections before they occur, especially in surgical procedures or after injuries.