Question

Choose the equation of a circle with radius 6 and center (2, -3).

Answer 1

Answer:  $(x-2)^2 + (y+3)^2 = 36$

Work Shown:

$(x-h)^2 + (y-k)^2 = r^2\\\\(x-2)^2 + (y-(-3))^2 = 6^2\\\\(x-2)^2 + (y+3)^2 = 36$

Note that (h,k) = (2,-3) is the center and r = 6 is the radius. The last line is not expanded out using the FOIL rule because its common practice to leave it in $(x-h)^2 + (y-k)^2 = r^2$ form. This form allows the reader to quickly determine the center and radius (rather than have to do a lot of algebraic steps before hand).