11. Analytic Geometry

Sketch a graph of the circle based on the following equation:

${(x-2)}^2+{(y+3)}^2=1$

Find the equation for the following circle:

Determine if the equation $x^3+y^2+4x-8y+4=0$ is a circle, and if it is, find its center and radius.

Determine if the equation $x^2+y^2-2x+4y-4=0$ is a circle, and if it is, find its center and radius.

Sketch a graph of the circle based on the following equation:

$x^2+{(y-1)}^2=9$