Center and radiusFind the center and radius of the circle whose equation is given by: (5 - x)^2 + (y - 1)^2 = 4

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to convert the given form of equation in standard form, on the coordinate plane, such that:

`(x - h)^2 + (y - k)^2 = R^2`

The center of circle is given by coordinates `x = h` and `y = k` and the radius is given by R.

Reasoning by analogy, yields:

`(5 - x)^2 + (y - 1)^2 = 4`

Since `(5 - x)^2 = (x - 5)^2` , you need to replace `(x - 5)^2` for `(5 - x)^2` such that:

`(x - 5)^2 + + (y - 1)^2 = 4 => (h,k) = (5,1),R^2 = 4 `

`(h,k) = (5,1),R = 2 `

Hence, evaluating the radius and center of circle yields `R = 2 ` and `(h,k) = (5,1)` .

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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The equation of the circle, whose radius is r and center of the circle is C(a,b):

(x-m)^2 + (y-n)^2 = r^2

Now, we'll write the given equation:

(5 - x)^2 + (y - 1)^2 = 4

[-(x-5)]^2 + (y - 1)^2 = 2^2

We'll identify the coordinates of the center of the circle as:

x coordinate:m = 5 and

y coordinate: n = 1

The center of the circle is C(5,1) and the radius is r = 2.

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