Answer: 18/5.
- A 18/5
- B 36/5
- C 9/5
- D 5/3
Correct answer: A. 18/5
Explanation: a=3, b=4, so c<sup>2</sup>=a<sup>2</sup>+b<sup>2</sup>=25, c=5, e=c/a=5/3. Directrices are at x=±a/e=±3/(5/3)=±9/5. Distance between the two directrices = 2(9/5) = 18/5.
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.