Question

the centre of a circle is at point o (-9, 8). point b is on the edge of this circle at (18, -2). what is the area of this circle? give your answer correct to 2 decimal places.

Explanation:

Step1: Calculate the radius

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $(x_1,y_1)=(-9,8)$ and $(x_2,y_2)=(18,-2)$.
$r=\sqrt{(18 - (-9))^2+(-2 - 8)^2}=\sqrt{(27)^2+(-10)^2}=\sqrt{729 + 100}=\sqrt{829}$

Step2: Calculate the area of the circle

The area formula of a circle is $A=\pi r^2$. Substitute $r = \sqrt{829}$ into the formula.
$A=\pi\times(\sqrt{829})^2=829\pi\approx 2604.18$

Answer:

$2604.18$