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What is the locus of a point for which y=b?
- a)A plane parallel to ZX plane at a distance b from it
- b)A plane parallel to YX plane at a distance b from it
- c)A plane parallel to YZ plane at a distance b from it
- d)A line parallel to X axis at a distance b from it
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the locus of a point for which y=b?a)A plane parallel to ZX pl...
Note: We have
- Plane | | to xy piane at a distance c, z = c
- Plane; | | to t/x plane ai a distance a, x = a
- Plane | to xx plane at a distance b ,y = b
Remark:- In particular, the equations of YZ, ZX and XY planes are x = 0, y = 0 and z = 0 respectively.
Most Upvoted Answer
What is the locus of a point for which y=b?a)A plane parallel to ZX pl...
Note: We have
- Plane | | to xy piane at a distance c, z = c
- Plane; | | to t/x plane ai a distance a, x = a
- Plane | to xx plane at a distance b ,y = b
Remark:- In particular, the equations of YZ, ZX and XY planes are x = 0, y = 0 and z = 0 respectively.
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What is the locus of a point for which y=b?a)A plane parallel to ZX pl...
Understanding the Locus of Points Where y = b
When analyzing the equation y = b, we need to comprehend what this signifies in a three-dimensional coordinate system.
Definition of the Locus
- The equation y = b indicates that for every point in space, the y-coordinate remains constant at the value b.
- This means that regardless of the values of x and z, the y value is fixed.
Visualization in 3D Space
- In a three-dimensional Cartesian coordinate system (X, Y, Z):
- The x-axis represents horizontal movement left or right.
- The z-axis represents depth movement forward or backward.
- The y-axis represents vertical movement up or down.
Implications of the Equation y = b
- Since y is constant, the locus of points can move freely along the x and z axes, while y remains at a fixed distance b.
- This creates a flat, infinite surface or plane.
Identifying the Correct Option
- The locus specified by y = b forms a plane in three-dimensional space:
- This plane is parallel to the xz-plane (the plane defined by the x and z axes).
- It exists at a distance b from the origin along the y-axis.
Conclusion
- Therefore, the correct answer is option 'A':
- A plane parallel to the XZ plane at a distance b from it.
This understanding of the locus of points is fundamental in geometry and aids in visualizing how fixed coordinates influence spatial relationships.
When analyzing the equation y = b, we need to comprehend what this signifies in a three-dimensional coordinate system.
Definition of the Locus
- The equation y = b indicates that for every point in space, the y-coordinate remains constant at the value b.
- This means that regardless of the values of x and z, the y value is fixed.
Visualization in 3D Space
- In a three-dimensional Cartesian coordinate system (X, Y, Z):
- The x-axis represents horizontal movement left or right.
- The z-axis represents depth movement forward or backward.
- The y-axis represents vertical movement up or down.
Implications of the Equation y = b
- Since y is constant, the locus of points can move freely along the x and z axes, while y remains at a fixed distance b.
- This creates a flat, infinite surface or plane.
Identifying the Correct Option
- The locus specified by y = b forms a plane in three-dimensional space:
- This plane is parallel to the xz-plane (the plane defined by the x and z axes).
- It exists at a distance b from the origin along the y-axis.
Conclusion
- Therefore, the correct answer is option 'A':
- A plane parallel to the XZ plane at a distance b from it.
This understanding of the locus of points is fundamental in geometry and aids in visualizing how fixed coordinates influence spatial relationships.
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What is the locus of a point for which y=b?a)A plane parallel to ZX plane ata distance b from itb)A plane parallel to YX plane ata distance b from itc)A plane parallel to YZplane ata distance b from itd)A line parallel to X axis at a distance b from itCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about What is the locus of a point for which y=b?a)A plane parallel to ZX plane ata distance b from itb)A plane parallel to YX plane ata distance b from itc)A plane parallel to YZplane ata distance b from itd)A line parallel to X axis at a distance b from itCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the locus of a point for which y=b?a)A plane parallel to ZX plane ata distance b from itb)A plane parallel to YX plane ata distance b from itc)A plane parallel to YZplane ata distance b from itd)A line parallel to X axis at a distance b from itCorrect answer is option 'A'. Can you explain this answer?.
What is the locus of a point for which y=b?a)A plane parallel to ZX plane ata distance b from itb)A plane parallel to YX plane ata distance b from itc)A plane parallel to YZplane ata distance b from itd)A line parallel to X axis at a distance b from itCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about What is the locus of a point for which y=b?a)A plane parallel to ZX plane ata distance b from itb)A plane parallel to YX plane ata distance b from itc)A plane parallel to YZplane ata distance b from itd)A line parallel to X axis at a distance b from itCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the locus of a point for which y=b?a)A plane parallel to ZX plane ata distance b from itb)A plane parallel to YX plane ata distance b from itc)A plane parallel to YZplane ata distance b from itd)A line parallel to X axis at a distance b from itCorrect answer is option 'A'. Can you explain this answer?.
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