Question

Transform the general equation of circle : x2 + y2 + 4x - 2y -11 =0 to its standard form or center-radius form. After transforming , identify the center and the radius then sketch the graph in the Cartesian coordinate plane .

Answer 1

Solution

For given equation

x² + y² + 4x - 2y - 11 = 0

x² + 4x + y² - 2y - 11 = 0

x² + 4x + 4 + y² - 2y + 1 - 11 – 5 = 0

(x + 2)² + (y - 1)² – 16 = 0

(x + 2)² + (y - 1)² = 4²  

It is equation of the circle with center (x_c,y_c) = (-2, 1) and radius r = 4.