Find the Circle Through (11,8) with Center (2,8) (2,8) , (11,8)

$(2, 8)$ , $(11, 8)$

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 $(2, 8)$ and $(11, 8)$ .

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.

$r = \sqrt{{(11 - 2)}^{2} + {(8 - 8)}^{2}}$

Simplify.

Subtract $2$ from $11$ .

$r = \sqrt{9^{2} + {(8 - 8)}^{2}}$

Raise $9$ to the power of $2$ .

$r = \sqrt{81 + {(8 - 8)}^{2}}$

Subtract $8$ from $8$ .

$r = \sqrt{81 + 0^{2}}$

Raising $0$ to any positive power yields $0$ .

$r = \sqrt{81 + 0}$

Add $81$ and $0$ .

$r = \sqrt{81}$

Rewrite $81$ as $9^{2}$ .

$r = \sqrt{9^{2}}$

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

$r = 9$

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, $r = 9$ and the center point is $(2, 8)$ . The equation for the circle is ${(x - (2))}^{2} + {(y - (8))}^{2} = {(9)}^{2}$ .

${(x - (2))}^{2} + {(y - (8))}^{2} = {(9)}^{2}$

Step 3

The circle equation is ${(x - 2)}^{2} + {(y - 8)}^{2} = 81$ .

${(x - 2)}^{2} + {(y - 8)}^{2} = 81$

Step 4

Find the Circle Through (11,8) with Center (2,8) (2,8) , (11,8)

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