CBSE Class 12 Mathematics 2026 Main Paper 65/5/2 · Q345 Marksellipse_area
CBSE Class 12 Mathematics 2026 Main Paper 65/5/2 · Question 34 (Applications Of Integrals)
Sketch 9x²+16y²=144 and use integration to find its enclosed area.
✅ Step-by-Step Solution
Final Answer: 12π square units.
- The ellipse x²/16+y²/9=1 has horizontal and vertical semiaxes 4 and 3.
- Use the upper branch y=(3/4)√(16−x²). By symmetry multiply its integral from 0 to 4 by four.
- The quarter-circle integral of √(16−x²) is 4π, so the area is 12π.
📋 CBSE Stepwise Marking Scheme
- [1 mark] The ellipse x²/16+y²/9=1 has horizontal and vertical semiaxes 4 and 3.
- [3 marks] Use the upper branch y=(3/4)√(16−x²). By symmetry multiply its integral from 0 to 4 by four.
- [1 mark] The quarter-circle integral of √(16−x²) is 4π, so the area is 12π.
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