1) $$ (x-2)^{2}+(y-5)^{2}=7^{2} $$

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The given equation $$ (x-2)^{2}+(y-5)^{2}=7^{2} $$ represents a circle in the Cartesian coordinate system.

### Known Conditions:
- The center of the circle is at the point $$ (2, 5) $$.
- The radius of the circle is $$ 7 $$.

### Step-by-Step Explanation:
1. **Identify the center and radius**:
   - The general form of a circle's equation is $$ (x-h)^{2} + (y-k)^{2} = r^{2} $$, where $$ (h, k) $$ is the center and $$ r $$ is the radius.
   - From the equation, we can see that:
     - $$ h = 2 $$
     - $$ k = 5 $$
     - $$ r = 7 $$

2. **Write the center and radius**:
   - Center: $$ (2, 5) $$
   - Radius: $$ 7 $$

### Conclusion:
The circle has a center at $$ (2, 5) $$ and a radius of $$ 7 $$. If you need further analysis or specific calculations related to this circle, please let me know!
The equation $$ (x-2)^{2}+(y-5)^{2}=7^{2} $$ represents a circle with center at $$ (2, 5) $$ and a radius of $$ 7 $$.

1) \( (x-2)^{2}+(y-5)^{2}=7^{2} \)

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