Q66.Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y−axis at C. The locus of the mid-point P of MC is (1) 3x2 + 2y −6 = 0 (2) 2x2 −3y + 9 = 0 (3) 3x2 −2y −6 = 0 (4) 2x2 + 3y −9 = 0
What This Question Tests
This question tests the ability to find the locus of a point by combining coordinate geometry concepts like midpoint, slope, perpendicular lines, and eliminating a parameter.
Concepts Tested
Formulas Used
M = ((x1+x2)/2, (y1+y2)/2)
Slope m = (y2-y1)/(x2-x1)
Perpendicular slope m' = -1/m
Equation of line: y - y1 = m(x - x1)
📚 NCERT Sections This Tests
2.3 — Two Charges 2 Mc And –2 Mc Are Placed At Points A And B 6 Cm
Physics Class 11 · Chapter 2
2.3 Two charges 2 mC and –2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
9.8 — A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 · Chapter 9
9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Locus, Straight Lines
- Year
- 2021
- Shift
- 27 Aug Shift 1
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines
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