Answer: Ellipse, e = 4/5.
- A Ellipse, e = 4/5
- B Ellipse, e = 3/5
- C Hyperbola, e = 4/5
- D Circle, e = 0
Correct answer: A. Ellipse, e = 4/5
Explanation: Dividing by 225: x<sup>2</sup>/25 + y<sup>2</sup>/9 = 1, an ellipse with a<sup>2</sup>=25, b<sup>2</sup>=9. c<sup>2</sup>=16, c=4, e=c/a=4/5.
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.