# Equation of a circle. Find the equation of a circle with center (5,-2) and radius 16.

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### 2 Answers

The equation of a circle with center (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2

Here the center is (5, -2) and the radius is 16

=> (x - 5)^2 + (y + 2)^2 = 16^2

=> x^2 + 25 - 10x + y^2 + 4 + 4y = 256

=> x^2 + y^2 - 10x + 4y - 227 = 0

**The equation of the required circle is x^2 + y^2 - 10x + 4y - 227 = 0**

The equation of the circle is:

(x - h)^2 + (y - k)^2 = r^2

The coordinates h and k represent the coordinates of the center of the circle.

We'll substitute the x and y coordinates of the center in the equation of the circle:

(x - 5)^2 + (y + 2)^2 = 16^2

(x - 5)^2 + (y + 2)^2 = 256

**The equation of the circle whose center is C(5 , -2) and radius , r = 16, is:**

**(x - 5)^2 + (y + 2)^2 = 256**