The locus of a point `P(x,y,z)` which moves in such away that `x=a`and `y=b` is a

Options

A. plane parallel to xy-plane
B. line parallel to x-axis
C. line parallel to y-axis
D. line parallel to z-axis

Explanation

To solve the problem of finding the locus of a point \( P(x, y, z) \) that moves such that \( x = a \) and \( y = b \), we can follow these steps:

### Step 1: Understand the conditions given
We are given that \( x = a \) and \( y = b \). This means that the coordinates of point \( P \) are constrained to specific values for \( x \) and \( y \).

### Step 2: Analyze the implications of the conditions
Since \( x \) is fixed at \( a \) and \( y \) is fixed at \( b \), the point \( P \) can take any value for \( z \). This means that the \( z \)-coordinate can vary freely while \( x \) and \( y \) remain constant.

### Step 3: Visualize the locus
The locus of points that satisfy these conditions can be visualized in three-dimensional space. Since \( x \) and \( y \) are constant, the point \( P \) will move vertically along the \( z \)-axis.

### Step 4: Describe the locus mathematically
The locus can be described as a line in three-dimensional space. Specifically, it is a vertical line where:
- \( x = a \)
- \( y = b \)
- \( z \) can take any real value.

### Conclusion
Thus, the locus of the point \( P(x, y, z) \) is a line parallel to the \( z \)-axis.

### Final Answer
The locus of the point \( P(x, y, z) \) is a line parallel to the \( z \)-axis.

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