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

1 Answer
Feb 8, 2016

#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#