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

Feb 5, 2016

The area of the circle described by your equation is $9 \pi {\text{ units"^2 ~~ 28.27 " units}}^{2}$.

#### Explanation:

The equation

${\left(x - 2\right)}^{2} + {\left(y + 4\right)}^{2} = 9$

describes a circle.

A standard circle equation for a circle with the center $\left(h , k\right)$ and the radius $r$ has the form

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

Thus, in your case, the center of your circle is the point $\left(2 , - 4\right)$ and your radius is $3$.

If I understand your question correctly, you would like to compute the area of this circle.

The formula for that is

$A = \pi {r}^{2} = \pi \cdot {3}^{2} = 9 \pi \approx 28.27 {\text{ units}}^{2}$