Q65.Let P be a variable point on the parabola y = 4x2 + 1. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is: (1) (3x −y)2 + (x −3y) + 2 = 0 (2) 2(3x −y)2 + (x −3y) + 2 = 0 (3) (3x −y)2 + 2(x −3y) + 2 = 0 (4) 2(x −3y)2 + (3x −y) + 2 = 0
What This Question Tests
The question asks for the locus of the midpoint between a variable point on a parabola and the foot of the perpendicular from that point to a given line. It requires using parametric form for the point, finding the foot of the perpendicular, and then applying the midpoint formula.
Concepts Tested
Formulas Used
Slope of perpendicular lines m1*m2 = -1
Midpoint formula ((x1+x2)/2, (y1+y2)/2)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Locus of a point
- Year
- 2021
- Shift
- 20 Jul Shift 2
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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