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The radius of a circle, having minimum a...

The radius of a circle, having minimum area, which touches the curve `y=4-x^2` and the lines `y=|x|` is :

A

`2 (sqrt(2) + 1)`

B

`2 (sqrt(2) - 1)`

C

`4 (sqrt(2) - 1)`

D

`4 (sqrt(2) + 1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the radius of circle with least area be r.
Then, then corrdinates of centre = (0, 4 - r) .

since, circle touches the line y = x in first quadrant
`:. |(0 - (4 - r))/(sqrt(2))| = r implies r - 4 = +- r sqrt(2)`
`implies r = (4)/(sqrt(2) + 1)` or `(4)/(1 - sqrt(2))`
But `r =! (4)/(1 - sqrt(2))` `[ :' (4)/(1 - sqrt(2)) lt 0]`
`:. r = (4)/(sqrt(2) + 1) = 4 (sqrt(2) - 1)`
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