Question

The area of the circle whose centre is at $(1,2)$ and which passes through the point $(4,6)$is:

• A. $5\pi$
• B. $10\pi$
• C. $25\pi$
• D. None of these

Answer 1

The correct option is C

$25\pi$

Explanation for the correct option:

Finding area of circle:

Given that centre $(1,2)$

And the point through which it passes is $(4,6)$

The distance between the centre and the given point is nothing but radius of cirlce

$$\begin{gathered} \Rightarrow r=\sqrt{(1-4{)}^2+(2-6{)}^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}$$

We know the area of circle $={\mathrm{\pi r}}^2$

$=\mathrm{\pi }{\left(5\right)}^2=25\mathrm{\pi }$ square unit

Hence, option C is the correct answer.