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x² + (y - 2)² = 100

Expand

x² + y ² - 4y + 4 = 100

x² + y ² - 4y - 96 = 0

comparing with the equation of a circle

x² + y² + 2gx + 2fy + c = 0

2g = 0 2f = - 4

g = 0 f = -2 c = - 96

center = ( - g , - f ) = ( 0 , 2)

To find the diameter first find the radius

radius = √ g ² + f² - c

= √ 0 +(-2)² + 96

= √ 4 + 96 = √ 100

= √ 10

Diameter = 2 × radius

= 2 × 10

= 20

Hope this helps.

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