What is the center and radius of the circle with the given equation (x - 1)² + (y + 1)² = 4

Solution:

Given, the equation is (x - 1)² + (y + 1)² = 4 --- (1)

We have to find the center and radius 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 = 1, b = -1

Coordinates of the center (a, b) = (1, -1)

r² = 4

r = 2

Radius of the circle r = 2

Therefore, the center and radius of the circle is (1, -1) and 2.

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What is the center and radius of the circle with the given equation (x - 1)² + (y + 1)² = 4

Summary:

The center and radius of the circle with the given equation (x - 1)² + (y + 1)² = 4 is (1, -1) and 2.