The equation of circle with centre (1, -2) and radius 4 cm is:

Given,

Centre of the circle (a, b) = (1, -2)

Radius of the circle (r) = 4 cm

$$\therefore\ $$Equation of the circle is $$\left(x-a\right)^2+\left(y-b\right)^2=r^2$$

$$=$$>  $$\left(x-1\right)^2+\left(y-\left(-2\right)\right)^2=4^2$$

$$=$$>  $$\left(x-1\right)^2+\left(y+2\right)^2=4^2$$

$$=$$>  $$x^2+1^2-2.x.1+y^2+2^2+2.y.2=16$$

$$=$$>  $$x^2+1-2x+y^2+4+4y=16$$

$$=$$>  $$x^2-2x+y^2+4y=16-1-4$$

$$=$$>  $$x^2+y^2-2x+4y=11$$

Hence, the correct answer is Option D