Answer: x 2 /25 + y 2 /16 = 1.
- A x<sup>2</sup>/25 + y<sup>2</sup>/9 = 1
- B x<sup>2</sup>/25 + y<sup>2</sup>/16 = 1
- C x<sup>2</sup>/16 + y<sup>2</sup>/25 = 1
- D x<sup>2</sup>/9 + y<sup>2</sup>/25 = 1
Correct answer: B. x<sup>2</sup>/25 + y<sup>2</sup>/16 = 1
Explanation: a=5, c=3, so b<sup>2</sup> = a<sup>2</sup>-c<sup>2</sup> = 25-9 = 16. Equation: x<sup>2</sup>/25 + y<sup>2</sup>/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.