How do you find the area of circle (x - 4)^2 + (y - 2)^2 = 9?

Feb 8, 2016

$9 \pi$

Explanation:

This is an equation of a circle in standard form. The equation

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

describes a circle with its center at the point $\left(h , k\right)$ and a radius $r$.

Since we want to find the area of this circle, all we need concern ourselves with is the circle's radius, since the area of a circle can be found through the formula

$A = \pi {r}^{2}$

From the equation of the circle, we can see that ${r}^{2} = 9$. Note that ${r}^{2}$ is already a term in the formula for the area of a circle, so we can plug it in straightaway:

$A = \pi {r}^{2} \text{ "=>" "A=pi(9)" "=>" } A = 9 \pi$