Answer: x2/16 - y2/9 = 1.
- A x2/16 - y2/9 = 1
- B x2/9 - y2/16 = 1
- C x2/16 + y2/9 = 1
- D x2/25 - y2/9 = 1
Correct answer: A. x2/16 - y2/9 = 1
Explanation: Foci (±5,0) means c=5. Transverse axis length=2a=8, so a=4, a²=16. b²=c²−a²=25−16=9. Standard form (foci on x-axis): x²/16−y²/9=1. Ans: x²/16−y²/9=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.