Q65.The point P(−2√6, √3) lies on the hyperbola x2a2 −y2b2 normal at P to the hyperbola intersect its conjugate axis at the points Q and R respectively, then QR is equal to: (1) 4√3 (2) 6 (3) 3√6 (4) 6√3
What This Question Tests
This question tests the ability to find the equations of tangent and normal to a hyperbola at a given point, determine their intersection with the conjugate axis, and calculate the distance between these intersection points.
Concepts Tested
Formulas Used
Equation of hyperbola: x²/a² - y²/b² = 1
Equation of tangent at (x₁,y₁): xx₁/a² - yy₁/b² = 1
Equation of normal at (x₁,y₁): a²x/x₁ + b²y/y₁ = a² + b²
📚 NCERT Sections This Tests
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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?
2.3 — Two Charges 2 Mc And –2 Mc Are Placed At Points A And B 6 Cm
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2.3 Two charges 2 mC and –2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
📋 Question Details
- Chapter
- Hyperbola
- Topic
- Tangent and Normal to Hyperbola
- Year
- 2021
- Shift
- 26 Aug Shift 2
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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