Find the equation of the circle having centre at `(3,-4)` and touching the line `5x+12 y-12=0.`

Explanation

To find the equation of the circle with a center at (3, -4) that touches the line given by the equation \(5x + 12y - 12 = 0\), we can follow these steps:

### Step 1: Identify the center of the circle
The center of the circle is given as \((h, k) = (3, -4)\).

### Step 2: Find the distance from the center to the line
To find the radius of the circle, we need to calculate the distance from the center of the circle to the line. The formula for the distance \(d\) from a point \((x_0, y_0)\) to the line \(Ax + By + C = 0\) is given by:

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