Q72.If the tangents drawn to the hyperbola 4y2 = x2+ 1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid point of AB is (1) x2 −4y2 + 16x2y2 = 0 (2) 4x2 −y2 + 16x2y2 = 0 (3) 4x2 −y2 −16x2y2 = 0 (4) x2 −4y2 −16x2y2 = 0
What This Question Tests
This question tests the ability to find the equation of a tangent to a hyperbola, determine its intercepts on the coordinate axes, and then derive the locus of the midpoint of these intercepts.
Concepts Tested
Formulas Used
Hyperbola: x²/a² - y²/b² = 1
Tangent at (x1, y1): xx1/a² - yy1/b² = 1
Midpoint (h, k)
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📋 Question Details
- Chapter
- Hyperbola
- Topic
- Locus of midpoint of tangent intercepts
- Year
- 2018
- Shift
- 15 Apr Shift 1 Online
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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