The point on a circle nearest to the point `P(2,1)` is at a distance of 4 units and the farthest point is (6, 5). Then find the equation of the circle.

Explanation

To find the equation of the circle based on the given information, we can follow these steps:

### Step 1: Identify the center of the circle
Given that the nearest point on the circle to the point \( P(2, 1) \) is at a distance of 4 units, we can denote the center of the circle as \( C(h, k) \). The distance from the center \( C(h, k) \) to the point \( P(2, 1) \) is given by the formula:

\[ \sqrt{(h - 2)^2 + (k - 1)^2} = r - d \]
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