Question

The area of the circle centred 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)

The equation of a circle centred at $(1,2)$ and passing through $(4,6)$ is
$(x-1)^{2}+(y-2)^{2}=(4-1)^{2}+(6-2)^{2}$
$\Rightarrow x^{2}+y^{2}-2 x-4 y+1+4=9+16$
$\Rightarrow x^{2}+y^{2}-2 x-4 y-20=0$
Now, radius $=\sqrt{(-1)^{2}+(-2)^{2}+20}$
$=\sqrt{1+4+20}=5$
$\therefore $ Area of circle $=\pi r^{2}$
$=25\,\pi$ sq unit