Q73.An ellipse passes through the foci of the hyperbola, 9x2 −4y2 = 36 and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is 1 , then which of the following points does not lie on the ellipse? 2 , (1) ( √392 √3) (2) ( √132 , √32 ) 2 , (3) (√13 (4) √6) (√13, 0) x is equal to
What This Question Tests
This question tests a deep understanding of properties of both hyperbolas and ellipses, specifically their foci, axes, and eccentricities, requiring calculations and point verification.
Concepts Tested
Formulas Used
Hyperbola x²/a² - y²/b² = 1, foci (±ae_h, 0), e_h = √(1 + b²/a²)
Ellipse x²/A² + y²/B² = 1, foci (±Ae_e, 0), e_e = √(1 - B²/A²) or (0, ±Be_e)
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
9.8 — A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 · Chapter 9
9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Ellipse
- Topic
- Properties of hyperbola and ellipse
- Year
- 2015
- Shift
- 10 Apr Online
- Q Number
- Q73
- Type
- Multi concept
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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