Question

Equation of the circle inscribed in $|x+1|+|y-6|=2$ is

• A. $(x-1{)}^2+(y-6{)}^2=2$
• B. $(x-1{)}^2+(y+6{)}^2=2$
• C. $(x+1{)}^2+(y-6{)}^2=2$
• D. $(x+1{)}^2+(y+6{)}^2=2$

Answer 1

The correct option is C $(x+1{)}^2+(y-6{)}^2=2$

$|x+1|+|y-6|=2$ is a square with centre $(-1,6)$ which is centre of the circle also.
Distance between two parallel sides $(x+1)+(y-6)=2$ and $(x+1)+(y-6)=-2$
i.e., $x+y=7$ and $x+y=3$ is $\left|\frac{-3+7}{\sqrt{2}}\right|=2\sqrt{2}$
$\therefore$ Radius of required circle $=\sqrt{2}$
Hence, equation of the circle is $(x+1{)}^2+(y-6{)}^2=2$