Question

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

Answer 1

`9pi`

Explanation:

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

`(x-h)^2+(y-k)^2=r^2`

describes a circle with its center at the point `(h,k)` 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=pir^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=pir^2" "=>" "A=pi(9)" "=>" "A=9pi`