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The Equation of circle for Circle B is (x - 2) ² + (y + 4)²  = 38.4.

For circle A:

Radius of circle A = √36 = 6

Area of circle A = π(6)^2 = 36π

Let's assume the radius of circle B is r.

Circumference of circle A = 2π(6) = 12π

Circumference of circle B = 3.2 x Circumference of circle A

= 3.2 x 12π

= 38.4π

Since the ratio of the areas is equal to the ratio of the circumferences, we have:

Area of circle B / Area of circle A = (r^2π) / (36π) = 38.4π / 36π

Simplifying, we get:

r² / 36 = 38.4 / 36

Cross-multiplying, we have:

36 x r² = 38.4 x 36

Dividing both sides by 36:

r^2 = 38.4

Taking the square root of both sides:

r = √38.4

Now we have the radius of circle B. Let's substitute this value into the equation for circle B:

(x - 2) ² + (y + 4)² = (√38.4)²

Simplifying:

(x - 2) ² + (y + 4)²  = 38.4

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