For the circle ##(x-1)^2 + (y+1)^2 = 20## in the ##xy##-plane, what is the coordinates of the center, the radius, and the area?

(1 ,-1) , ##2sqrt5 , 20pi≈62.83##

The of a circle is

##color(red)(|bar(ul(color(white)(a/a)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(a/a)|)))## where (a ,b) are the coords of centre and r, the radius

now ##(x-1)^2+(y+1)^2=20" is in this form"##

and by comparison: a = 1 , b = -1 and ##r^2=20 ##

centre = (a ,b) = (1 -1) , r##=sqrt20=2sqrt5##

and area##=pir^2=pixx(sqrt20)^2=20pi ≈62.83##