The locus of a point `P(x,y,z)` which moves in such a way that `z=c` (constant), is a

Options

A. a. line parallel to z-axis
B. b. plane parallel to xy-plane
C. c.line parallel to y-axis
D. d.line parallel to x-axis

Explanation

To find the locus of a point \( P(x, y, z) \) that moves such that \( z = c \) (where \( c \) is a constant), we can follow these steps:

### Step 1: Understand the given condition
The condition given is \( z = c \). This means that the \( z \)-coordinate of the point \( P \) is fixed at a constant value \( c \).

### Step 2: Analyze the implications of the condition
Since \( z \) is constant, the point \( P \) can take any value for \( x \) and \( y \). Therefore, the coordinates of the point can be expressed as \( P(x, y, c) \).

### Step 3: Visualize the locus
The locus of the point \( P \) can be visualized in three-dimensional space. Since \( x \) and \( y \) can vary freely while \( z \) remains constant at \( c \), the locus forms a plane.

### Step 4: Identify the type of plane
The plane is parallel to the \( xy \)-plane because it has the same orientation as the \( xy \)-plane but is located at a height \( z = c \).

### Conclusion
Thus, the locus of the point \( P(x, y, z) \) that moves such that \( z = c \) is a plane parallel to the \( xy \)-plane at a height \( z = c \).

### Final Answer
The locus is a plane parallel to the \( xy \)-plane at \( z = c \).

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