Answer: x = ±25/4.
- A x = ±25/4
- B x = ±20/4
- C x = ±4/25
- D x = ±9/4
Correct answer: A. x = ±25/4
Explanation: Directrices are x = ±a/e. With a=5 and e=4/5, x = ±5/(4/5) = ±25/4.
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.