Find the Equation of the Circle (0,5) , r=1/2

$(0, 5)$ , $r = \frac{1}{2}$

Step 1

The standard form of a circle is $x^{2}$ plus $y^{2}$ equals the radius squared $r^{2}$ . The horizontal $h$ and vertical $k$ translations represent the center of the circle. The formula is derived from the distance formula where the distance between the center and every point on the circle is equal to the length of the radius.

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

Step 2

Fill in the values of $h$ and $k$ which represent the center of the circle.

${(x - 0)}^{2} + {(y - 5)}^{2} = r^{2}$

Step 3

Fill in the value of $r$ which represents the radius of the circle.

${(x - 0)}^{2} + {(y - 5)}^{2} = {(\frac{1}{2})}^{2}$

Step 4

Simplify.

Simplify the left side of the equation.

Multiply $- 1$ by $0$ .

${(x + 0)}^{2} + {(y - 5)}^{2} = {(\frac{1}{2})}^{2}$

Add $x$ and $0$ .

$x^{2} + {(y - 5)}^{2} = {(\frac{1}{2})}^{2}$

Simplify ${(\frac{1}{2})}^{2}$ .

Apply the product rule to $\frac{1}{2}$ .

$x^{2} + {(y - 5)}^{2} = \frac{1^{2}}{2^{2}}$

One to any power is one.

$x^{2} + {(y - 5)}^{2} = \frac{1}{2^{2}}$

Raise $2$ to the power of $2$ .

$x^{2} + {(y - 5)}^{2} = \frac{1}{4}$

Step 5

Find the Equation of the Circle (0,5) , r=1/2

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