Answer:
Center:(-6,-4)
Circumference:45.31
Area:163.4
Step-by-step explanation:
The given circle has diameter with endpoints P(-12,-8) and Q(0,0).
The center is the midpoint of P(-12,-8) and Q(0,0).
We use the midpoint rule to find the center.
[tex]( \frac{x_2+x_1}{2}, \frac{y_2+y_1}{2} )[/tex]
[tex]( \frac{ - 12 + 0}{2} , \frac{ - 8 + 0}{2} ) = ( - 6, - 4)[/tex]
Use the distance formula to find radius using the center (-6,-4) and the point on the circle (0,0) or (-12,-8).
[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2} [/tex]
[tex]r = \sqrt{( { - 6 - 0)}^{2} + ( { - 4 - 0)}^{2} } [/tex]
[tex]r = \sqrt{36 + 16} = \sqrt{52} [/tex]
The circumference is
[tex]C=2\pi \: r[/tex]
[tex]C=2 \: \pi \: \times \sqrt{52} [/tex]
[tex]C=45.31 \: units[/tex]
The area is given by:
[tex]A=\pi {r}^{2} [/tex]
[tex]A=\pi \times {( \sqrt{52} )}^{2} [/tex]
[tex]A=163.4 \: \: {units}^{2} [/tex]
