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(A) The equation of the common chord of two circles $S_1 = 0$ and $S_2 = 0$ is given by $S_1 - S_2 = 0$.Given circles are:$S_1: (x - a)^2 + (y - b)^2

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$x - y = 0$

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(A) The equation of the common chord of two circles $S_1 = 0$ and $S_2 = 0$ is given by $S_1 - S_2 = 0$.Given circles are:$S_1: (x - a)^2 + (y - b)^2 - c^2 = 0$$S_2: (x - b)^2 + (y - a)^2 - c^2 = 0$Subtracting $S_2$ from $S_1$:$((x - a)^2 - (x - b)^2) + ((y - b)^2 - (y - a)^2) = 0$Expanding the terms:$(x^2 - 2ax + a^2 - (x^2 - 2bx + b^2)) + (y^2 - 2by + b^2 - (y^2 - 2ay + a^2)) = 0$$(-2ax + a^2 + 2bx - b^2) + (-2by + b^2 + 2ay - a^2) = 0$Simplifying the expression:$2bx - 2ax + 2ay - 2by = 0$$2(b - a)x - 2(b - a)y = 0$Dividing by $2(b - a)$ (assuming $a 
eq b$):$x - y = 0$

The equation of the common chord of the circles $(x - a)^2 + (y - b)^2 = c^2$ and $(x - b)^2 + (y - a)^2 = c^2$ is

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