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 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 and the line equation
The center of the circle is given as \(C(3, -4)\) and the line equation is \(5x + 12y - 12 = 0\).

### Step 2: Use the distance formula to find the radius
The radius of the circle is equal to the distance from the center of the circle to the line. The formula for the distance \(d\) from a point \((x_1, y_1)\) to the line \(Ax + By + C = 0\) is given by:

...