Question

Equation of the circle inscribed in $|x-2|+|y-5|=4$ is

• A. $(x-2{)}^2+(y+5{)}^2=8$
• B. $(x+2{)}^2+(y-5{)}^2=8$
• C. $(x-2{)}^2+(y-5{)}^2=8$
• D. $(x-2{)}^2+(y-5{)}^2=4$

Answer 1

The correct option is C $(x-2{)}^2+(y-5{)}^2=8$

$|x-2|+|y-5|=4$ is a square with centre $(2,5)$ which is centre of the circle also.
Distance between two parallel sides $(x-2)+(y-5)=4$ and $(x-2)+(y-5)=-4$
i.e., $x+y=11$ and $x+y=3$ is
$\left|\frac{-11+3}{\sqrt{2}}\right|=4\sqrt{2}$
$\therefore$ Radius of the required circle $=2\sqrt{2}$
Hence, equation of the circle is $(x-2{)}^2+(y-5{)}^2=(2\sqrt{2}{)}^2=8$