Which equation is the equation of a circle with a diameter of 20 cm and center at (-3, 6) ?

A. (x-3) ^2 + (y+6) ^2 = 400

B. (x-3) ^2 + (y+6) ^2 = 100

C. (x+3) ^2 + (y-6) ^2 = 100

D. (x+3) ^2 + (y-6) ^2 = 400

The equation of a circle with centre (a, b) and radius r is:

(x - a) ^2 + (y - b) ^2 = r^2

thus,

here centre (a, b) = (-3,6), a = - 3, b = 6

and radius = diameter/2 = 20/2 = 10 units

therefore, the equation is

(x + 3) ^2 + (y - 6) ^2 = 100

which is c.