Question

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

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

Answer 1

The correct option is C $25$ $\pi$

The centre of the circle is $(1,2)$.

$(x-1{)}^2+(y-2{)}^2=a^2$

It passes through $(4,6)$.

Therefore, $(4-1{)}^2+(6-2{)}^2=a^2$

$\Rightarrow a^2=9+16$

$\Rightarrow a=5$

Thus radius $a=5$

Hence, area of circle is $\pi a^2=\pi (5{)}^2=25\pi$