# circleFind the equation of the circle whose center (0,13) and the area = 25pi.

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### 2 Answers

The area of a circle is pi*r^2. As the area of the circle to be found is 25pi.

pi*r^2 = 25*pi

=> r = 5

The equation of a circle with center (0, 13) and radius 5 is:

(x - 0)^2 + (y - 13)^2 = 5^2

=> x^2 + y^2 + 169 - 26y = 25

=> x^2 + y^2 - 26y + 144 = 0

**The equation of the circle is x^2 + y^2 - 26y + 144 = 0**

(x-h)^2 + (y-k)^2 = r^2, h and k are the coordinates of the center of the circle.

We'll identify h and k:

h = 0 and k = 13

Now, we'll use the formula of area of the circle to determine the radius of the circle:

A = pi*r^2

25*pi = pi*r^2

We'll divide by pi:

r^2 = 25

r = 5

We'll reject the negative value.

Now,we'll substitute the coordinates of the center of the circle and the value of radius in the equation of the circle:

x^2 + (y - 13)^2 = 25

If we'll expand the square, we'll obtain the general form of the equation:

x^2 + y^2 - 26y + 169 - 25 = 0

**x^2 + y^2 - 26y + 144 = 0**