Find the equation of the circle which passes through the points `(1,-2),(4,-3)` and whose center lies on the line `3x+4y=7.`

Explanation

To find the equation of the circle that passes through the points (1, -2) and (4, -3) with its center lying on the line \(3x + 4y = 7\), we can follow these steps:

### Step 1: General Equation of the Circle
The general equation of a circle can be expressed as:
\[ x^2 + y^2 + 2gx + 2fy + c = 0 \]
where \((-g, -f)\) is the center of the circle.
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