Equation of circle inscribed in `|x-a| +|y-b| =1` is

Options

A. `(x+a)^(2) + (y+b)^(2) =2`
B. `(x-a)^(2) +(y-b)^(2) = (1)/(2)`
C. `(x-a)^(2) +(y-b)^(2) = (1)/(sqrt(2))`
D. `(x-a)^(2) +(y-b)^(2) = 1`

Answer

B

Explanation

`|x -a| + |y-b| =1` is square with center at (a,b) which is the center of circle also.
Distance between two parallel sides of square is `sqrt(2)`.
`:.` Radius of the required circle `= (1)/(sqrt(2))`
Hence, equation of circle is `(x-a)^(2)+(y-b)^(2) =(1)/(2)`