Question

How do you find the center and radius for `(x-2)^2+ (y+7)^2 =40`?

Answer 1

centre = (2 ,-7)
radius = `2sqrt10`

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 coordinates of the centre and r, the radius.

The equation here `(x-2)^2+(y+7)^2=40" is in this form"`

and by comparison : a = 2 , b = -7 and `r^2=40`

`rArr" centre" =(2,-7)" and " r=sqrt40=2sqrt10`