Answer:
100π units square
Step-by-step explanation:
The circle is centered on the point (-1,5) and contains the point (7,11).
We can find the radius, using the distance formula,
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We substitute the points to get:
[tex]r=\sqrt{(7- - 1)^2+(11- 5)^2}[/tex]
This implies that:
[tex]r=\sqrt{(8)^2+(6)^2}[/tex]
[tex]r=\sqrt{64+36}[/tex]
[tex]r = \sqrt{100} [/tex]
[tex]r = 10 \: units[/tex]
The area of a circle is given by:
[tex]A=\pi \: {r}^{2} [/tex]
Plug in the radius into the formula to get:
[tex]A=\pi \times {10}^{2} [/tex]
[tex]A=\pi \times 100[/tex]
[tex]A=100\pi[/tex]
The area is 100π square units or 314 square units
