what is the center and radius of this circle

Question

(x-5)^ + (y+2)^=16

Answer 1

Given equation of a circle (x - 5)^2 + (y + 2)^2 = 16

Standard equation of a circle (x - h)^2 + (y - k)^2 = r^2

For standard equation of circle centre = (h , k) and radius = r

Compare the given equation of circle with standard equation of circle

Here h = 5 and k = -2 and r = sqrt(16)

Therefore centre = (5 , -2) and radius = sqrt(16) = 4

 

 

Answer 2

Given circle ( x - 5 )^2 + ( y + 2 )^2 = 16

=> ( x - 5 )^2 + ( y + 2 )^2 = 4^2-----------(2)

Compare this circle equation with standerd circle i.e, (x - h)^2 + (y - k)^2 = r^2-----------(2)

Where (h,k) is the center and " r " is the radius

Therefore compare (1) and (2)

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

Therefore center (h,k) = (5,-2) and radius r = 4