Write an equation of the circle whose center shifted 1 unit to the left and 2 units up from the origin and its circumference is 16 pi.

Answer 1

Circles are of the form (x-a)² + (y-b)² = r², where (a,b) is the center and r is the radius.

Because of this transformation, the center is at (-1,2). So to begin, our equation will start as (x-(-1))² + (y-2)² = r², which is the same as (x+1)² + (y-2)² = r².

Now we must find the radius of this circle. We know the circumference is 16π and the circumference equation is C=2πr. Thus we can do the following computations:

C = 2πr

16π = 2πr

16 = 2r (pi's cancel out)

r = 8 (divide by 2 on both sides)

We need r² which is 8² which is 64. So our final equation is:

(x+1)² + (y-2)² = 64