The equation of a circle whose centre is $(3, -1)$ and which intercept chord of $6$ units length on straight line $2x - 5y + 18 = 0$ is

The distance from the center (3, -1) to the line 2x - 5y + 18 = 0 is d = |2(3) - 5(-1) + 18| / sqrt(2^2 + (-5)^2) = |6 + 5 + 18| / sqrt(29) = 29 / sqrt(29) = sqrt(29). The chord length is 6, so half-length is 3. Radius r satisfies r^2 = d^2 + 3^2 = 29 + 9 = 38. Equation: (x-3)^2 + (y+1)^2 = 38, which is x^2 - 6x + 9 + y^2 + 2y + 1 = 38, or x^2 + y^2 - 6x + 2y - 28 = 0.