Question

How do you find the center of the radius of `(x-1)^2 + (y+2)^2 =25`?

Answer 1

centre = (1 ,-2) and radius = 5

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 `(x-1)^2+(y+2)^2=25" is in this form"`

and by comparison with the standard form we obtain.

a = 1 , b = -2 and r = 5

Hence centre = (a ,b) = (1 ,-2) and radius = 5