What is the locus of a point for which x = a and y= b?a)a line parallel to XY planeb)a plane parallel to XY planec)a line parallel to z-axisd)a plane perpendicular tpo XY planeCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Locus of a point refers to the set of all points that satisfy a given condition or set of conditions. In this case, we are given that x = a and y = b. We need to determine the locus of points that satisfy these conditions.

To understand the locus, let's consider the coordinate system with the x-axis, y-axis, and z-axis. The x-axis represents the horizontal axis, the y-axis represents the vertical axis, and the z-axis represents the axis perpendicular to the XY plane.

The point (x, y, z) represents a point in the three-dimensional space. In this case, we are given that x = a and y = b. This means that the x-coordinate of the point is fixed at a, and the y-coordinate of the point is fixed at b.

The locus of points that satisfy these conditions is a line parallel to the z-axis. This can be understood as follows:

- Since the x-coordinate is fixed at a, all possible points will have the same x-coordinate of a.
- Similarly, since the y-coordinate is fixed at b, all possible points will have the same y-coordinate of b.
- However, the z-coordinate can vary freely, meaning the points can have any value for the z-coordinate.
- Therefore, the locus of points satisfying x = a and y = b is a line parallel to the z-axis, as the points can have any value for the z-coordinate while maintaining the fixed x and y coordinates.

Hence, the correct answer is option C) a line parallel to the z-axis.

Answer

x = a is a plane | | to YZ plane
y = b is a plane | | to ZX plane
Therefore x = a and y = b is a line parallel to z-axis
Note : Remember that two planes intersect in a line

Answer

x = a is a plane | | to YZ plane
y = b is a plane | | to ZX plane
Therefore x = a and y = b is a line parallel to z-axis
Note : Remember that two planes intersect in a line

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