Find the locus of a point which moves such that its distance from x axis is five times its distance from y axis.

Answer

To find the locus of a point that moves such that its distance from the x-axis is five times its distance from the y-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Point**: Let the point be represented as \( (H, K) \).

2. **Understand Distances**: The distance from the x-axis is given by the y-coordinate, which is \( K \). The distance from the y-axis is given by the x-coordinate, which is \( H \).

3. **Set Up the Relationship**: According to the problem, the distance from the x-axis (which is \( K \)) is five times the distance from the y-axis (which is \( H \)). This can be expressed mathematically as:
\[ K = 5H \]

4. **Replace Variables**: To express the locus in standard coordinate form, we can replace \( H \) and \( K \) with \( x \) and \( y \) respectively. Thus, we rewrite the equation:
\[ y = 5x \]

5. **Conclusion**: The locus of the point is the line represented by the equation:
\[ y = 5x \]