Find the equation of the circle which touches the lines `4x-3y+10=0a n d4x-3y-30=0` and whose centre lies on the line `2x+y=0.`

Explanation

To find the equation of the circle that touches the lines \(4x - 3y + 10 = 0\) and \(4x - 3y - 30 = 0\) and whose center lies on the line \(2x + y = 0\), we can follow these steps:

### Step 1: Identify the lines
The two lines given are:
1. \(L_1: 4x - 3y + 10 = 0\)
2. \(L_2: 4x - 3y - 30 = 0\)

These lines are parallel since they have the same coefficients for \(x\) and \(y\).
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