Question 636292
The equation of the circle can be expressed as {{{(x + 3)^2 + (y - 1)^2 = 16}}}.
The center of the circle {{{(x-h)^2 + (y-k)^2 = r^2}}} is (h,k) and the radius is r. Therefore, the center of the circle {{{(x + 3)^2 + (y - 1)^2 = 16}}} is  (-3,1).

The slope of line joining (1,-2) and (-3,1) is
{{{m = (1-(-2))/(-3-1) = -3/4}}}
The equation of the diameter is
{{{ y - (-2) = (-3/4)(x - 1)}}}
Answer: {{{highlight(y = (-3/4)x - 5/4)}}}