Q69.If a tangent to the circle x2 + y2 = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is: (1) x2 + y2–16x2y2 = 0 (2) x2 + y2–4x2y2 = 0 (3) x2 + y2–2xy = 0 (4) x2 + y2–2x2y2 = 0
What This Question Tests
This question integrates concepts from circles and straight lines. It requires finding the equation of a tangent to a circle, determining its intercepts on the coordinate axes, and then finding the locus of the midpoint of these intercepts through algebraic elimination.
Concepts Tested
Formulas Used
Equation of tangent at (x1, y1) to x²+y²=r² is xx1+yy1=r²
Intercept form x/a + y/b = 1
Midpoint formula
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📋 Question Details
- Chapter
- Circles
- Topic
- Tangent to a circle, locus
- Year
- 2019
- Shift
- 09 Apr Shift 1
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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