Q84.Let an ellipse with centre (1, 0) and latus rectum of length 21 have its major axis along x-axis. If its minor axis subtends an angle 60∘ at the foci, then the square of the sum of the lengths of its minor and major axes is equal to _______.
What This Question Tests
This question tests the understanding of various properties of an ellipse, including its latus rectum, eccentricity, and the geometric interpretation of the minor axis subtending an angle at the foci, requiring simultaneous equations to solve for 'a' and 'b'.
Concepts Tested
Formulas Used
2b²/a = L
b² = a²(1 - e²)
tan(θ) = y/x
📚 NCERT Sections This Tests
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9.21 At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.
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📋 Question Details
- Chapter
- Ellipse
- Topic
- Properties of Ellipse
- Year
- 2023
- Shift
- 15 Apr Shift 1
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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