Write the equation of the circle with center (2, -3) and a radius of 4.

Solution:

The equation of a circle is

(x - h)² + (y - k)² = r²

Where (h, k) is the center

r is the radius

It is given that

Center = (2, -3)

Radius = 4

Substituting the values in the formula

(x - 2)² + (y - (-3))² = 4²

(x - 2)²  + (y + 3)² = 16

Expanding using the algebraic identity

(a - b)² = a² + b² - 2ab

(a + b)² = a² + b² + 2ab

We get

x² + 4 - 4x + y² + 9 + 6y = 16

x² + y² - 4x + 6y = 16 - 13

x² + y² - 4x + 6y = 3

Therefore, the equation of the circle is x² + y² - 4x + 6y = 3.

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Write the equation of the circle with center (2, -3) and a radius of 4.

Summary:

The equation of the circle with center (2, -3) and a radius of 4 is x² + y² - 4x + 6y = 3.