Precalculus Examples

(0, 0)

$(0, 0)$ ,

(- 6, 6)

$(- 6, 6)$

Step 1

Find the radius

r

$r$ for the circle. The radius is any line segment from the center of the circle to any point on its circumference. In this case,

r

$r$ is the distance between

(0, 0)

$(0, 0)$ and

(- 6, 6)

$(- 6, 6)$ .

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Step 1.1

Use the distance formula to determine the distance between the two points.

Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 1.2

Substitute the actual values of the points into the distance formula.

r = \sqrt{{((- 6) - 0)}^{2} + {(6 - 0)}^{2}}

$r = \sqrt{{((- 6) - 0)}^{2} + {(6 - 0)}^{2}}$

Step 1.3

Simplify.

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Step 1.3.1

Subtract

0

$0$ from

- 6

$- 6$ .

r = \sqrt{{(- 6)}^{2} + {(6 - 0)}^{2}}

$r = \sqrt{{(- 6)}^{2} + {(6 - 0)}^{2}}$

Step 1.3.2

Raise

- 6

$- 6$ to the power of

2

$2$ .

r = \sqrt{36 + {(6 - 0)}^{2}}

$r = \sqrt{36 + {(6 - 0)}^{2}}$

Step 1.3.3

Subtract

0

$0$ from

6

$6$ .

r = \sqrt{36 + 6^{2}}

$r = \sqrt{36 + 6^{2}}$

Step 1.3.4

Raise

6

$6$ to the power of

2

$2$ .

r = \sqrt{36 + 36}

$r = \sqrt{36 + 36}$

Step 1.3.5

Add

36

$36$ and

36

$36$ .

r = \sqrt{72}

$r = \sqrt{72}$

Step 1.3.6

Rewrite

72

$72$ as

6^{2} \cdot 2

$6^{2} \cdot 2$ .

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Step 1.3.6.1

Factor

36

$36$ out of

72

$72$ .

r = \sqrt{36 (2)}

$r = \sqrt{36 (2)}$

Step 1.3.6.2

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

r = \sqrt{6^{2} \cdot 2}

$r = \sqrt{6^{2} \cdot 2}$

r = \sqrt{6^{2} \cdot 2}

$r = \sqrt{6^{2} \cdot 2}$

Step 1.3.7

Pull terms out from under the radical.

r = 6 \sqrt{2}

$r = 6 \sqrt{2}$

r = 6 \sqrt{2}

$r = 6 \sqrt{2}$

r = 6 \sqrt{2}

$r = 6 \sqrt{2}$

Step 2

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

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ is the equation form for a circle with

r

$r$ radius and

(h, k)

$(h, k)$ as the center point. In this case,

r = 6 \sqrt{2}

$r = 6 \sqrt{2}$ and the center point is

(0, 0)

$(0, 0)$ . The equation for the circle is

{(x - (0))}^{2} + {(y - (0))}^{2} = {(6 \sqrt{2})}^{2}

${(x - (0))}^{2} + {(y - (0))}^{2} = {(6 \sqrt{2})}^{2}$ .

{(x - (0))}^{2} + {(y - (0))}^{2} = {(6 \sqrt{2})}^{2}

${(x - (0))}^{2} + {(y - (0))}^{2} = {(6 \sqrt{2})}^{2}$

Step 3

The circle equation is

{(x - 0)}^{2} + {(y - 0)}^{2} = 72

${(x - 0)}^{2} + {(y - 0)}^{2} = 72$ .

{(x - 0)}^{2} + {(y - 0)}^{2} = 72

${(x - 0)}^{2} + {(y - 0)}^{2} = 72$

Step 4

Simplify the circle equation.

x^{2} + y^{2} = 72

$x^{2} + y^{2} = 72$

Step 5

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