# Circle equation.Determine the equation of the circle whose circumference is 14*pi and the center is (3,-2).

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The circumference of a circle is 2*pi*r.

Here the circumference is 14*pi

2*pi*r = 14*pi

=> r = 7

The equation of the circle with center (3 , -2) and radius 7 is

(x - 3)^2 + (y + 2)^2 = 49

=> x^2 + 9 - 6x + y^2 + 4 + 4y = 49

=> x^2 + y^2 - 6x + 4y - 36 = 0

**The equation of the required circle is x^2 + y^2 - 6x + 4y - 36 = 0**

The circumference of the circle is L = 2*pi*r.

We'll putĀ l = 14

14*pi = 2*pi*r

r = 7

Since we know the coordinates of the center of the circle and the radius, we'll write the equation in the standard form:

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

All we need to do is to substitute the values of the coordinates of the center and the value of the radius into the equation:

(x - 3)^2 + (y + 2)^2 = 7^2

**The requested equation of the circle is: (x - 3)^2 + (y + 2)^2 = 7^2**