Question

which equation represents a circle with the same center as the circle shown but with a radius of 2 units?
$\big(x-4\big)^2+\big(y-5\big)^2=2$
$\big(x-4\big)^2+\big(y-5\big)^2=4$
$\big(x-5\big)^2+\big(y-4\big)^2=2$
$\big(x-5\big)^2+\big(y-4\big)^2=4$

Explanation:

Step1: Identify circle center

From the graph, the center $(h,k)$ is $(4,5)$.

Step2: Recall circle equation formula

The standard circle equation is $(x-h)^2+(y-k)^2=r^2$, where $r$ is radius.

Step3: Substitute $r=2$ and center

Substitute $h=4$, $k=5$, $r=2$:
$(x-4)^2+(y-5)^2=2^2$
Simplify: $(x-4)^2+(y-5)^2=4$

Answer:

B. $(x - 4)^2 + (y - 5)^2 = 4$