the equation of a circle is x² + y² - 4x + 2y - 31 = 0. what is the center and the radius of the circle? show your work.

centre = (2, - 1), radius = 6

Step-by-step explanation:

Rearrange the equation by placing the x and y terms together and adding 31 to both sides

Given

x² + y² - 4x + 2y - 31 = 0, then

x² - 4x + y² + 2y = 31

Use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1

(x - 2)² + (y + 1)² = 36

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

compare to (x - 2)² + (y + 1)² = 36, then

centre = (2, - 1) and r = = 6

69

step-by-step explanation: