Identify the center of the circle whose equation is (x - 2)² + (y + 8)² = 16.

Solution:

A circle is defined as the locus of a moving point on a plane such that its distance from a fixed point on the plane remains constant or fixed. 

That fixed point is called the center of the circle.

Given, the equation of the circle is (x - 2)² + (y + 8)² = 16. ----------------- (1)

We have to find the center of the circle.

The standard form of the equation of a circle is given by

(x - a)² + (y - b)² = r² -------------------------- (2)

Where, a and b are the coordinates of the centre

r is the radius

Comparing (1) and (2)

a = 2

b = -8

r = 4

Therefore, the center of the circle is (2, -8).

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Identify the center of the circle whose equation is (x - 2)² + (y + 8)² = 16.

Summary:

The center of the circle whose equation is (x - 2)² + (y + 8)² = 16 is (2, -8).