Answer: x2/25 + y2/16 = 1.
- A x2/25 + y2/9 = 1
- B x2/25 + y2/16 = 1
- C x2/16 + y2/25 = 1
- D x2/9 + y2/25 = 1
Correct answer: B. x2/25 + y2/16 = 1
Explanation: a=5, c=3, so b2 = a2-c2 = 25-9 = 16. Equation: x2/25 + y2/16 = 1.
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.