Not sure how to do this. ?

a.

Distance between any point (x, y) on the circle and the center (h. k) = Radius of the circle
√[(x - h)² + (y - k)²] = r
{√[(x - h)² + (y - k)²]}² = r²
(x - h)² + (y - k)² = r²

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b.
(x - h)² + (y - k)² = r²
[x - (-3)]² + (y - 5)² = 2²
(x + 3)² + (y - 5)² = 4
x² + y² + 6x - 10y + 30 = 0

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c.
After magnified by a factor of 5, radius = 5
After shifted 4 units right and 7 units down, center = (4, -7)

Equation of the circle:
(x - 4)² + [y - (-7)]² = 5²
(x - 4)² + (y + 7)² = 25
x² + y² - 8x + 14y + 40 = 0

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d.
Radius, r
= √16
= 4

Arc length
= rθ
= 4 × (2π/3)
= 8π/3 (units)