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QUESTION

# 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