Joint equation of co-ordinates axes, in a plane is

Options

A. `x^(2)-y^(2)=0`
B. `x^(2)+y^(2)=1`
C. `xy=0`
D. `xy=x+y`

Answer

To find the joint equation of the coordinate axes in a plane, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Coordinate Axes**:
- The x-axis is represented by the equation \(y = 0\) (where the y-coordinate is always zero).
- The y-axis is represented by the equation \(x = 0\) (where the x-coordinate is always zero).

2. **Write the Individual Equations**:
- For the x-axis:
\[ y = 0 \]
- For the y-axis:
\[ x = 0 \]

3. **Combine the Equations**:
- To find the joint equation, we need to combine these two equations. A common method to combine equations is to multiply them.
- Multiply the equations \(y = 0\) and \(x = 0\):
\[ (y)(x) = 0 \]

4. **Final Joint Equation**:
- The joint equation of the coordinate axes is:
\[ xy = 0 \]

### Summary:
The joint equation of the coordinate axes in a plane is given by:
\[ xy = 0 \]