Q10.Let the ellipse E1 : x2a2 + y2b2 A2 √3 product of their lengths of latus rectums be 32 , and the distance between the foci of E1 be 4. If E1 and E2 √3 meet at A, B, C and D , then the area of the quadrilateral ABCD equals : (1) 12√6 (2) 6√6 5 (3) 18√6 (4) 24√6 5 5
What This Question Tests
This question requires a thorough understanding of various properties of ellipses, including eccentricity, latus rectum, and foci, to derive the equations of two ellipses and then calculate the area of the quadrilateral formed by their intersection points.
Concepts Tested
Formulas Used
e = √(1 - b²/a²)
Length of latus rectum = 2b²/a
Distance between foci = 2ae
Area of rhombus = (1/2)d₁d₂
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📋 Question Details
- Chapter
- Ellipse
- Topic
- Properties of Ellipse
- Year
- 2025
- Shift
- 29 Jan Shift 1
- Q Number
- Q10
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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