Question

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Question- Write the standard form equation of the circle given the center of (-1,0) and the circumference of 8π. Show all work using the equation editor to calculate the missing pieces of the equation.

Answer 1

Answer: (x+1)^2 + (y-0)^2 = 8pi^2

Step-by-step explanation:

Answer 2

To determine the standard form equation of the circle with center (-1,0) and circumference of 8π, the radius is found to be 4, leading to the equation (x + 1)² + y² = 16.

Step-by-step explanation:

To find the standard form equation of the circle with the center at (-1,0) and a circumference of 8π, we first need to determine the radius. The formula for circumference is C = 2πr, which allows us to solve for the radius r. Given that the circumference is 8π, we set up the equation 8π = 2πr and solve for r:

1. Divide both sides by 2π to isolate r:
2. r = 8π / 2π
3. r = 4

With a radius of 4, we can write the standard form equation of the circle: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Substituting the center (-1,0) and radius 4, the equation becomes:

(x + 1)² + y² = 4²

(x + 1)² + y² = 16

This is the standard form equation of the circle in question.