The radius of a circle, having minimum area, which touches the curve `y=4−x^2` and the lines, `y=|x|` is: (a) `4(sqrt2+1)` (b) `2(sqrt2+1)` (c) `2(sqrt2-1)` (d) `4(sqrt2-1)`

Explanation

C(0,4-r)

y-x=0

`|(4-r-0)/sqrt2|=r`

`4-r=pmsqrt2r`

`4=(sqrt2+1)r`

`r=4/(sqrt2+1)*(sqrt2-1)/(sqrt2-1)`

`=(4(sqrt2-1))/(2-1)`

Option 1 is correct.