Find the locus of point whose distance from the origin is 5.

Answer

To find the locus of a point whose distance from the origin is 5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the locus of points that are at a distance of 5 units from the origin (0, 0).

2. **Define the Point**: Let the point in question be represented as \( (h, k) \).

3. **Apply the Distance Formula**: The distance \( d \) from the origin to the point \( (h, k) \) can be calculated using the distance formula:
\[ d = \sqrt{(h - 0)^2 + (k - 0)^2} = \sqrt{h^2 + k^2} \]

4. **Set the Distance Equal to 5**: According to the problem, this distance is given to be 5:
\[ \sqrt{h^2 + k^2} = 5 \]

5. **Square Both Sides**: To eliminate the square root, we square both sides of the equation:
\[ h^2 + k^2 = 5^2 \]
\[ h^2 + k^2 = 25 \]

6. **Replace Variables**: Since \( h \) and \( k \) are arbitrary points, we can replace them with \( x \) and \( y \) respectively:
\[ x^2 + y^2 = 25 \]

7. **Interpret the Result**: The equation \( x^2 + y^2 = 25 \) represents a circle centered at the origin (0, 0) with a radius of 5.

### Final Answer:
The locus of the point whose distance from the origin is 5 is the equation of a circle:
\[ x^2 + y^2 = 25 \]