Q5. A rod of length eight units moves such that its ends A and B always lie on the lines x −y + 2 = 0 and y + 2 = 0, respectively. If the locus of the point P , that divides the rod AB internally in the ratio 2 : 1 is 9 (x2 + αy2 + βxy + γx + 28y) −76 = 0, then α −β −γ is equal to : (1) 22 (2) 21 (3) 23 (4) 24
What This Question Tests
This problem involves setting up coordinates for the ends of a moving rod based on the lines they lie on, using the section formula to find the coordinates of point P, and then eliminating the parameters to find the locus equation.
Concepts Tested
Formulas Used
Section formula: P((mx2+nx1)/(m+n), (my2+ny1)/(m+n))
Distance formula: sqrt((x2-x1)^2 + (y2-y1)^2)
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📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Locus problems
- Year
- 2025
- Shift
- 23 Jan Shift 2
- Q Number
- Q5
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines
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