JEE Main 2021 — Circle Question with Solution

Given, the equation of circle is $x^2+y^2-2x-6y+6=0$

So, the centre of the circle is $\left(1,3\right)$ and the radius is $\sqrt{1^2+3^2-6}=2$

Assume, the coordinate of point $B$ is $\left(-1,k\right)$ and the coordinate of point $A$ is $\left(h,1\right).$

So, $\sqrt{{\left(h+1\right)}^2}=2\Rightarrow h=1$ and $\sqrt{{\left(k-1\right)}^2}=2\Rightarrow k=3$

So, the coordinate of $B$ is $\left(-1,3\right)$ and the coordinate of $A$ is $\left(1,1\right).$

From the diagram, area of $∆ABD=\frac{1}{2}\times 2\times 4$

$=4$ sq. units