center and radius

Question

 State the center and the radius of the circle represented by the equation. show all work 

 

(x-4)^2+(y+6)^2=64

Answer 1

(x-4)^2 + (y+6)^2 = 64

 

(x–4)^2 + (y–(-6))^2 = 8^2

 

Center: (4,–6)

Radius: 8

 

Because:

 

Using Pythagorean Theorem you can find the equation of a circle centered at origin with radius r as:

 

x^2 + y^2 = r^2

 

Then you can translate it <h,k> (h units in x-direction, k units in y-direction) to get:

 

(x – h)^2 + (y – k)^2 = r^2