Q25.Let H1 : x2a2 −y2b2 A2 B2 and e2 respectively. If the product of the lengths of 12√5 respectively. Let their ecentricities be e1 = √52 their transverse axes is 100√10, then 25e22 is equal to ________.
What This Question Tests
This question involves manipulating the properties of two different hyperbolas, setting up and solving a system of equations based on their latus rectum, eccentricity, and transverse axis lengths.
Concepts Tested
Formulas Used
e^2 = 1 + b^2/a^2 (for x^2/a^2 - y^2/b^2 = 1)
e^2 = 1 + a^2/b^2 (for y^2/b^2 - x^2/a^2 = 1)
Latus Rectum = 2b^2/a (for x^2/a^2 - y^2/b^2 = 1)
Latus Rectum = 2a^2/b (for y^2/b^2 - x^2/a^2 = 1)
Transverse axis length = 2a (for x^2/a^2 - y^2/b^2 = 1)
Transverse axis length = 2b (for y^2/b^2 - x^2/a^2 = 1)
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
2.5 — A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 · Chapter 2
2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
12.7 — The Radius Of The Innermost Electron Orbit Of A Hydrogen Atom Is
Physics Class 12 · Chapter 12
12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?
📋 Question Details
- Chapter
- Hyperbola
- Topic
- Properties of hyperbola
- Year
- 2025
- Shift
- 24 Jan Shift 2
- Q Number
- Q25
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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