Find the Circle Through (-3,2) with Center (4,-3) (-3,2) , (4,-3)

$(- 3, 2)$ , $(4, - 3)$

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 $(4, - 3)$ and $(- 3, 2)$ .

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.

$r = \sqrt{{((- 3) - 4)}^{2} + {(2 - (- 3))}^{2}}$

Simplify.

Subtract $4$ from $- 3$ .

$r = \sqrt{{(- 7)}^{2} + {(2 - (- 3))}^{2}}$

Raise $- 7$ to the power of $2$ .

$r = \sqrt{49 + {(2 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$r = \sqrt{49 + {(2 + 3)}^{2}}$

Add $2$ and $3$ .

$r = \sqrt{49 + 5^{2}}$

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

$r = \sqrt{49 + 25}$

Add $49$ and $25$ .

$r = \sqrt{74}$

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, $r = \sqrt{74}$ and the center point is $(4, - 3)$ . The equation for the circle is ${(x - (4))}^{2} + {(y - (- 3))}^{2} = {(\sqrt{74})}^{2}$ .

${(x - (4))}^{2} + {(y - (- 3))}^{2} = {(\sqrt{74})}^{2}$

Step 3

The circle equation is ${(x - 4)}^{2} + {(y + 3)}^{2} = 74$ .

${(x - 4)}^{2} + {(y + 3)}^{2} = 74$

Step 4

Find the Circle Through (-3,2) with Center (4,-3) (-3,2) , (4,-3)

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