Question

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

• A. $5\mathrm{\pi }\mathrm{sq}\mathrm{units}$
• B. $10\mathrm{\pi }\mathrm{sq}\mathrm{units}$
• C. $25\mathrm{\pi }\mathrm{sq}\mathrm{units}$
• D. None of these

Answer 1

The correct option is C

$25\mathrm{\pi }\mathrm{sq}\mathrm{units}$

Explanation for Correct Answer:

The circle is centred and$(1,2)$and passing through $(4,6)$.

Let the center of a circle is $O(1,2)$ and the passing point is $P(4,6)$.

Hence $OP$ is a radius of a given circle.

Therefore radius $OP$ is equal to

$$\begin{gathered} OP=\sqrt{{\left(4-1\right)}^2+{\left(6-2\right)}^2} \\ =\sqrt{3^2+4^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}$$

Now area of a given circle is

$$\begin{gathered} Area={\mathrm{\pi r}}^2 \\ =\mathrm{\pi }\times 5^2\left[\because \mathrm{r}=\mathrm{OP}=5\right] \\ =25\mathrm{\pi } \end{gathered}$$

Therefore the area of a given circle is equal to $25\mathrm{\pi }$ $squareunits$.

Hence, option (C) is correct.