Find the Circle Through (-1,5) with Center (5,-3) (-1,5) , (5,-3)

$(- 1, 5)$ , $(5, - 3)$

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 $(5, - 3)$ and $(- 1, 5)$ .

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.

$r = \sqrt{{((- 1) - 5)}^{2} + {(5 - (- 3))}^{2}}$

Simplify.

Subtract $5$ from $- 1$ .

$r = \sqrt{{(- 6)}^{2} + {(5 - (- 3))}^{2}}$

Raise $- 6$ to the power of $2$ .

$r = \sqrt{36 + {(5 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$r = \sqrt{36 + {(5 + 3)}^{2}}$

Add $5$ and $3$ .

$r = \sqrt{36 + 8^{2}}$

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

$r = \sqrt{36 + 64}$

Add $36$ and $64$ .

$r = \sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$r = \sqrt{10^{2}}$

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

$r = 10$

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, $r = 10$ and the center point is $(5, - 3)$ . The equation for the circle is ${(x - (5))}^{2} + {(y - (- 3))}^{2} = {(10)}^{2}$ .

${(x - (5))}^{2} + {(y - (- 3))}^{2} = {(10)}^{2}$

Step 3

The circle equation is ${(x - 5)}^{2} + {(y + 3)}^{2} = 100$ .

${(x - 5)}^{2} + {(y + 3)}^{2} = 100$

Step 4

Find the Circle Through (-1,5) with Center (5,-3) (-1,5) , (5,-3)

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