Match the following curves in Column I with their eccentricities in Column II.
Step-by-Step Solution
Key Concept: Use standard eccentricity formulas: ellipse e = √(1 - b²/a²), hyperbola e = √(1 + b²/a²), parabola e = 1.
Step 1: P: Ellipse a²=16, b²=9, e = √(1 - 9/16) = √7/4 => matches 2. Step 2: Q: Hyperbola a²=16, b²=9, e = √(1 + 9/16) = 5/4 => matches 3. Step 3: R: Parabola y² = 16x => e = 1 => matches 1. Step 4: S: Parabola x² = 4y => e = 1 => matches 1.
Correct Answer: [P-2] [Q-3] [R-1] [S-1]