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?

Answer 1

(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`