Q71.If the tangent drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinates axes at the distinct points A and B, then the locus of the midpoint of AB is : (1) x2 −4y2 + 16x2y2 = 0 (2) 4x2 −y2 + 16x2y2 = 0 (3) x2 −4y2 −16x2y2 = 0 (4) 4x2 −y2 −16x2y2 = 0
What This Question Tests
This question requires finding the equation of a tangent to a hyperbola, determining its intercepts with the coordinate axes, and then finding the locus of the midpoint of the segment formed by these intercepts.
Concepts Tested
Formulas Used
Hyperbola: x²/a² - y²/b² = 1
Tangent y = mx ± √(a²m² - b²)
Midpoint formula: ((x1+x2)/2, (y1+y2)/2)
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📋 Question Details
- Chapter
- Hyperbola
- Topic
- Tangent to hyperbola, locus of a midpoint
- Year
- 2018
- Shift
- 15 Apr
- Q Number
- Q71
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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