Question

The area of the circle whose centre is at $(1, 2) $ and passing through $(4, 6)$ is

• A. $5 \pi$ sq unit
• B. $10 \pi$ sq unit
• C. $25 \pi$ sq unit
• D. none of these

Answer 1

Answer: (C)

Area of circle $=\pi r^{2}$
The centre of circle is $(1,2)$ and point on the circle is $(4,6)$.
Radius $=$ distance between centre and point on. Circle
$=\sqrt{(4-1)^{2}+(6-2)^{2}}=\sqrt{3^{2}+4^{2}}$
$=5$
As we know Radius of circle $=\pi r^{2}$ $=\pi(5)^{2}$
$=25 \pi$ sq unit