Equation of XY-plane is

Options

A. z=0
B. x=0
C. y=0
D. `ax+by+d=0`

Answer

To find the equation of the XY-plane, we can follow these steps:

### Step 1: Understand the definition of the XY-plane
The XY-plane is defined as the plane where all points have a z-coordinate of zero. This means that for any point (x, y, z) in the XY-plane, the value of z is always 0.

### Step 2: Write the general equation of a plane
The general equation of a plane in three-dimensional space can be expressed as:
\[ Ax + By + Cz = D \]
where A, B, C, and D are constants.

### Step 3: Substitute the values for the XY-plane
For the XY-plane, since z is always 0, we can substitute C = 1 and D = 0. Thus, the equation simplifies to:
\[ 0x + 0y + 1z = 0 \]
or simply:
\[ z = 0 \]

### Step 4: Identify the correct option
From the options provided:
- Option A: \( z = 0 \)
- Option B: \( x = 0 \)
- Option C: \( y = 0 \)
- Option D: \( Ax + By + D = 0 \)

The equation \( z = 0 \) corresponds to the XY-plane.

### Conclusion
Thus, the equation of the XY-plane is:
\[ z = 0 \]

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