Answer: x2/25 + y2/16 = 1.
- A x2/25 + y2/16 = 1
- B x2/16 + y2/25 = 1
- C x2/9 + y2/25 = 1
- D x2/25 + y2/9 = 1
Correct answer: A. x2/25 + y2/16 = 1
Explanation: Foci at (±3,0) means c=3. Eccentricity e=c/a=3/5, so a=c/e=3÷(3/5)=5; a²=25. Then b²=a²−c²=25−9=16. Equation: x²/25+y²/16=1. Ans: 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.