Find the Circle Using the Diameter End Points

$(- 3, - 4)$ , $(- 1, - 2)$

Step 1

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. The given end points of the diameter are $(- 3, - 4)$ and $(- 1, - 2)$ . The center point of the circle is the center of the diameter, which is the midpoint between $(- 3, - 4)$ and $(- 1, - 2)$ . In this case the midpoint is $(- 2, - 3)$ .

Tap for more steps...

Step 1.1

Use the midpoint formula to find the midpoint of the line segment.

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Step 1.2

Substitute in the values for $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

$(\frac{- 3 - 1}{2}, \frac{- 4 - 2}{2})$

Step 1.3

Subtract $1$ from $- 3$ .

$(\frac{- 4}{2}, \frac{- 4 - 2}{2})$

Step 1.4

Divide $- 4$ by $2$ .

$(- 2, \frac{- 4 - 2}{2})$

Step 1.5

Cancel the common factor of $- 4 - 2$ and $2$ .

Tap for more steps...

Step 1.5.1

Factor $2$ out of $- 4$ .

$(- 2, \frac{2 \cdot - 2 - 2}{2})$

Step 1.5.2

Factor $2$ out of $- 2$ .

$(- 2, \frac{2 \cdot - 2 + 2 \cdot - 1}{2})$

Step 1.5.3

Factor $2$ out of $2 \cdot - 2 + 2 \cdot - 1$ .

$(- 2, \frac{2 \cdot (- 2 - 1)}{2})$

Step 1.5.4

Cancel the common factors.

Tap for more steps...

Step 1.5.4.1

Factor $2$ out of $2$ .

$(- 2, \frac{2 \cdot (- 2 - 1)}{2 (1)})$

Step 1.5.4.2

Cancel the common factor.

$(- 2, \frac{2 \cdot (- 2 - 1)}{2 \cdot 1})$

Step 1.5.4.3

Rewrite the expression.

$(- 2, \frac{- 2 - 1}{1})$

Step 1.5.4.4

Divide $- 2 - 1$ by $1$ .

$(- 2, - 2 - 1)$

Step 1.6

Subtract $1$ from $- 2$ .

$(- 2, - 3)$

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Simplify.

Tap for more steps...

Step 2.3.1

Multiply $- 1$ by $- 2$ .

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

Step 2.3.2

Add $- 3$ and $2$ .

$r = \sqrt{{(- 1)}^{2} + {((- 4) - (- 3))}^{2}}$

Step 2.3.3

Raise $- 1$ to the power of $2$ .

$r = \sqrt{1 + {((- 4) - (- 3))}^{2}}$

Step 2.3.4

Multiply $- 1$ by $- 3$ .

$r = \sqrt{1 + {(- 4 + 3)}^{2}}$

Step 2.3.5

Add $- 4$ and $3$ .

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

Step 2.3.6

Raise $- 1$ to the power of $2$ .

$r = \sqrt{1 + 1}$

Step 2.3.7

Add $1$ and $1$ .

$r = \sqrt{2}$

Step 3

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ is the equation form for a circle with $r$ radius and $(h, k)$ as the center point. In this case, $r = \sqrt{2}$ and the center point is $(- 2, - 3)$ . The equation for the circle is ${(x - (- 2))}^{2} + {(y - (- 3))}^{2} = {(\sqrt{2})}^{2}$ .

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

Step 4

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

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

Step 5

Enter YOUR Problem

Find the Circle Using the Diameter End Points

Conic Sections

How to Use Step-by-Step Examples

Why use Mathway?

Explore More Algebra Help