Question

question 10 of 10
the centre of a circle is at point o (-10, 18). point b (1, -3) is on the circumference of this circle. what is the area of this circle? give your answer correct to 2 decimal places.

Explanation:

Step1: Calculate the radius

The distance between the center $O(-10,18)$ and a point $B(1, - 3)$ on the circumference is the radius $r$. Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-10,y_1 = 18,x_2=1,y_2=-3$.
$r=\sqrt{(1-(-10))^2+(-3 - 18)^2}=\sqrt{(1 + 10)^2+(-21)^2}=\sqrt{121 + 441}=\sqrt{562}$.

Step2: Calculate the area of the circle

The area formula of a circle is $A=\pi r^2$. Substitute $r = \sqrt{562}$ into the formula.
$A=\pi\times(\sqrt{562})^2=562\pi\approx562\times3.14159 = 1765.57358\approx1765.57$.

Answer:

$1765.57$