Question

The circle below is centered at the point (4,1) and has a radius of length 2. What is its equation?

Answer 1

Answer:

$(x-4)^{2}+(y-1)^{2} =4$

Step-by-step explanation:

we know that

The equation of a circle in center radius form is equal to

$(x-h)^{2}+(y-k)^{2} =r^{2}$

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

$(h,k)=(4,1)$

$r=2\ units$

substitute

$(x-4)^{2}+(y-1)^{2} =2^{2}$

$(x-4)^{2}+(y-1)^{2} =4$

Answer 2

If (x0,y0) is the center point of a circle, then

(x - x0)^2 + (y - y0)^2 = r^2

the equation is (x-4)^2 + (y-1)^2 = 4