1. a) Let $x^{2}+y^{2}-a x+b y=c$ be the equation of a circle with centre $(2,3)$ and radius 4 . Find the values of $a, b$ and $c$.

Step 1 ：Given the equation of a circle with center (2, 3) and radius 4, we can write the equation as \((x - 2)^2 + (y - 3)^2 = 4^2\)

Step 2 ：Expanding the equation, we get \(x^2 - 4x + y^2 - 6y - 3\)

Step 3 ：Comparing the expanded equation with the given equation \(x^2 + y^2 - ax + by = c\), we find the values of a, b, and c

Step 4 ：\boxed{a = 4, b = -6, c = -3}