Q69.If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from O on AB is : (1) (x2 + y2)(x + y) = R2xy (2) (x2 + y2)3 = 4R2x2y2 (3) (x2 + y2) 2 = 4R2x2y2 (4) (x2 + y2) 2 = 4Rx2y2
What This Question Tests
This problem is multi-conceptual, requiring the use of circle properties (diameter formed by axis intercepts), straight line equations, perpendicularity conditions, and algebraic manipulation to derive the locus.
Concepts Tested
Formulas Used
Equation of line x/a + y/b = 1
m1*m2 = -1 for perpendicular lines
Pythagorean theorem for diameter (a²+b²=(2R)²)
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📋 Question Details
- Chapter
- Circles
- Topic
- Locus of foot of perpendicular from origin
- Year
- 2019
- Shift
- 12 Jan Shift 2
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (Circles)
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