Using the following equation, find the center and radius of the circle. you must show all work and calculations to receive credit. x2 − 4x + y2 + 8y = −4

centre = (2, - 4 ) and radius = 4

the equation of a circle in standard form is

( x - a )² + ( y - b )² = r²

where (a , b ) are the coordinates of the centre and r is the radius

to obtain this form use the method of ' completing the square ' on both the x and y terms.

x² + 2(- 2 )x + 4 + y² +2( 4)y + 16 = -4 + 4 + 16

(x - 2 )² + (y + 4 )² = 16 ( in standard form ), thus

centre = (2 , - 4 ) and r = √16 = 4