consider a family of circles passing through two fixed points `S(3,7)` and `B(6,5)`. If the common chords of the circle `x^(2)+y^(2)-4x-6y-3=0` and the members of the family of circles pass through a fixed point (a,b), then

Explanation

To solve the problem, we need to find the fixed point (a, b) through which the common chords of the given circle and the family of circles pass. Here’s a step-by-step solution:

### Step 1: Find the equation of the line passing through points S(3, 7) and B(6, 5)

The slope \( m \) of the line through points \( S(3, 7) \) and \( B(6, 5) \) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 7}{6 - 3} = \frac{-2}{3}
...