When The circle below is centered at the point (2 -3) and has a radius of length 4. What is its equation?

Using Pythagoras.

( x - 2)^" + ( y - - 3)^2 = 4^2

Becomes

(x - 2)^2 + (y + 3)^2 = 4^2

This can be expanded to : - #

x^2 - 4x + 4 + y^2 + 6y + 9 = 16

Collecting terms.

x^2 + y^2 - 4x + 6y - 3 = 0