Find the center and the radius of the circle x 22 y 42 25

Find the center and the radius of the circle.

(x + 2)^2 + (y + 4)^2 =25

Solution

For a center (h,k) and radius \'r\' ,the equation of a circle is in the form of (x-h)² + (y-k)² = r²

Given circle equation is (x + 2)^2 + (y + 4)^2 =25

It can be writtten as the general circle equation and thus we can find out center and radius.

(x+2)² + (y+4)² = 25

(x-(-2))² + (y-(-4))² = 5²

Compare it with (x-h)² + (y-k)² = r²

h=-2 ,k=-4 ,r=5

So, Center (h,k) =(-2,-4)

Radius (r) =5

Therefore, (x + 2)^2 + (y + 4)^2 =25 has Center =(-2,-4) and Radius =5.