Write the equation of the circle, x^2 + y^2 - 4x - 2y - 4 = 0, in standard form.

Question

I know that the formula is r = √(x-h)^2 + (y - k)^2 but i get confused with the values of center and all, please help. Thank you!

Answer 1

The equation is equavilent to:

 

(x^2-4x+4)+(y^2-2y+1)-9 = 0

(x-2)^2+(y-1)^2 = 9 = 3^2

 

This is a circle that is centered at (2,1) with radius 3

Answer 2

x² - 4x        + y² - 2y       = 4              Use completion of the square

x² - 4x + 4 + y² - 2y + 1 = 4+ 4 + 1

(x - 2)² + (y - 1)² = 9                          Center at (2, 1) radius 3