# Circle Graph

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A circle is the set of all points in a plane which are at a constant distance from a fixed point in the plane. A fixed point is called the 'center' and the constant distance is called the radius of the circle.

A circle has an eccentricity of zero, so the eccentricity shows you how "un-circular" the curve is. Bigger eccentricities are less curved. The standard equation of circle with center as origin (0,0)is given by

**x**

^{2}+ y^{2}= r^{2}**Examples on circle graph**

The equation of circle is x

^{2}+ y

^{2}= 4

^{2}where radius is 2. So the graph will look like :

The standard equation of circle with center as (h,k) is given by

**(x - h)**where h and k are the center of the circle.

^{2}+ (y - k)^{2}= r^{2}**Example :**

**(x - 2)**

^{2}+ (y - 1)^{2}= 5^{2}Here the center of the circle is (2,1) and radius is 5.So the graph will be

**Examples**

1) Find the equation of the circle with center(-3,2) and radius 5.

**Solution :**

Here, the center (h,k) is (-3,2) and radius is 5. Hence, substituting, h= -3 and k = 2 and r = 5 in

(x - h)

^{2}+ (y - k)

^{2}= r

^{2}

[x-(-3)]

^{2}+ (y - 2)

^{2}= 5

^{2}

⇒ (x+3)

^{2}+ (y-2)

^{2}= 25.

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2) Find the center and radius of the circle. x

^{2}+ y

^{2}-2x + 4y = 8

**Solution :**

The given equation is (x

^{2}-2x)+ y

^{2}+ 4y ) = 8

Now, completing the square within the parenthesis, we get

(x

^{2}- 2x + 1) +(y

^{2}+4y + 4) = 8 + 1 + 4

(x -1)

^{2}+ (y + 2)

^{2}= (√13)

^{2}

Comparing it with the equation of the circle, we see that the center of the circle is (1,-2) and radius is √13.

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**circle graph**

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