Solution for Problem 2.4.2

Find the equation in general form of a circle with the center at (4, -1) and radius of  5.

Solve

Step

r = 5 and (h, k) = (4, -1) Plug in the values 
(x - h)2 + (y - k)2 = r2  Use Standard Equation form
(x - 4)2 + (y - (-1))2 = 52  Simplify 
(x - 4)2 + (y + 1)2 = 25  Put in general form
x2 - 8x + 16 + y+ 2y + 1 = 25 Multiply out
x2 + y2 - 8x + 2y + 17 = 25 Combine like terms and reorder terms
x2 + y2 - 8x + 2y  - 8 = 0 Set equal to zero for general form
General Form: x2 + y2 + cx + dy + e = 0