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
$(x-1{)}^2+(y-2{)}^2=(4-1{)}^2+(6-2{)}^2$
$\Rightarrow x^2+y^2-2x-4y+1+4=9+16$
$\Rightarrow x^2+y^2-2x-4y-20=0$
Now, radius $=\sqrt{(-1{)}^2+(-2{)}^2+20}$
$=\sqrt{1+4+20}=5$
$\therefore$ Area of circle $=\pi r^2$
$=25\pi$ sq unit