Find the equation of the circle having `(1,-2)` as its centre and passing through the intersection of the lines `3x+y=14and2x+5y=18.`

Explanation

To find the equation of the circle with center (1, -2) that passes through the intersection of the lines \(3x + y = 14\) and \(2x + 5y = 18\), we can follow these steps:

### Step 1: Find the intersection point of the lines
We have two equations:
1. \(3x + y = 14\) (Equation 1)
2. \(2x + 5y = 18\) (Equation 2)

We can solve these equations simultaneously. Let's express \(y\) from Equation 1:
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