Answer: 5/4.
- A 3/4
- B 4/3
- C 5/4
- D 5/3
Correct answer: C. 5/4
Explanation: a<sup>2</sup>=16, b<sup>2</sup>=9, c<sup>2</sup>=a<sup>2</sup>+b<sup>2</sup>=25, c=5. Eccentricity e = c/a = 5/4.
All four conics form a single family distinguished only by eccentricity: a circle is the most "closed" (e=0), an ellipse is an elongated closed curve, a parabola is the borderline open curve (e=1), and a hyperbola has two separate open branches (e>1).
Concept context
Study circles, parabolas, ellipses, and hyperbolas as curves formed by intersecting a plane with a double cone, with their standard equations and key properties.