Find the Circle Through (-7,-1) with Center (8,7) (-7,-1) , (8,7)

$(- 7, - 1)$ , $(8, 7)$

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 $(8, 7)$ and $(- 7, - 1)$ .

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.

$r = \sqrt{{((- 7) - 8)}^{2} + {((- 1) - 7)}^{2}}$

Simplify.

Subtract $8$ from $- 7$ .

$r = \sqrt{{(- 15)}^{2} + {((- 1) - 7)}^{2}}$

Raise $- 15$ to the power of $2$ .

$r = \sqrt{225 + {((- 1) - 7)}^{2}}$

Subtract $7$ from $- 1$ .

$r = \sqrt{225 + {(- 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$r = \sqrt{225 + 64}$

Add $225$ and $64$ .

$r = \sqrt{289}$

Rewrite $289$ as $17^{2}$ .

$r = \sqrt{17^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$r = 17$

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, $r = 17$ and the center point is $(8, 7)$ . The equation for the circle is ${(x - (8))}^{2} + {(y - (7))}^{2} = {(17)}^{2}$ .

${(x - (8))}^{2} + {(y - (7))}^{2} = {(17)}^{2}$

Step 3

The circle equation is ${(x - 8)}^{2} + {(y - 7)}^{2} = 289$ .

${(x - 8)}^{2} + {(y - 7)}^{2} = 289$

Step 4

Find the Circle Through (-7,-1) with Center (8,7) (-7,-1) , (8,7)

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