Show that the line `3x - 4y -c = 0` will meet the circle having centre at (2, 4) and the radius 5 in real and distinct points if `-35 lt c lt 15`.

Explanation

To show that the line \(3x - 4y - c = 0\) meets the circle with center at \((2, 4)\) and radius \(5\) in real and distinct points when \(-35 < c < 15\), we will follow these steps:

### Step 1: Write the equation of the circle
The equation of a circle with center \((h, k)\) and radius \(r\) is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
For our circle, the center is \((2, 4)\) and the radius is \(5\). Thus, the equation of the circle is:
...