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 Answer
May 14, 2016

(1 ,-1) , #2sqrt5 , 20pi≈62.83#

Explanation:

The standard form of the equation 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#