A circle x^2 + y^ + 2x - 2y -1 = 0 expressed in the following form (x-h)^2 + (y-k)^2 = r^2 where h, k are the coordinates of the centre. How is r the radius given?
Rearrange into incomplete quadratics:
(x² + 2x) + (y² - 2y) = 1
Complete the squares:
(x² + 2x + 1) + (y² - 2y + 1) = 1 + 1 + 1
Express in the required form:
(x + 1)² + (y - 1)² = (√3)²
Thus: h = -1, k = 1, r = √3