Find the Circle Through (-2,1) with Center (-6,6) (-6,6) , (-2,1)

$(- 6, 6)$ , $(- 2, 1)$

Step 1

Find the radius $r$ for the circle. The radius is any line segment from the center of the circle to any point on its circumference. In this case, $r$ is the distance between $(- 6, 6)$ and $(- 2, 1)$ .

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

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

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

$r = \sqrt{{((- 2) - (- 6))}^{2} + {(1 - 6)}^{2}}$

Simplify.

Multiply $- 1$ by $- 6$ .

$r = \sqrt{{(- 2 + 6)}^{2} + {(1 - 6)}^{2}}$

Add $- 2$ and $6$ .

$r = \sqrt{4^{2} + {(1 - 6)}^{2}}$

Raise $4$ to the power of $2$ .

$r = \sqrt{16 + {(1 - 6)}^{2}}$

Subtract $6$ from $1$ .

$r = \sqrt{16 + {(- 5)}^{2}}$

Raise $- 5$ to the power of $2$ .

$r = \sqrt{16 + 25}$

Add $16$ and $25$ .

$r = \sqrt{41}$

Step 2

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ is the equation form for a circle with $r$ radius and $(h, k)$ as the center point. In this case, $r = \sqrt{41}$ and the center point is $(- 6, 6)$ . The equation for the circle is ${(x - (- 6))}^{2} + {(y - (6))}^{2} = {(\sqrt{41})}^{2}$ .

${(x - (- 6))}^{2} + {(y - (6))}^{2} = {(\sqrt{41})}^{2}$

Step 3

The circle equation is ${(x + 6)}^{2} + {(y - 6)}^{2} = 41$ .

${(x + 6)}^{2} + {(y - 6)}^{2} = 41$

Step 4

Find the Circle Through (-2,1) with Center (-6,6) (-6,6) , (-2,1)

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