Two equal circles of largest radii have following property:
(i) They intersect each other orthogonally,
(ii) They touch both the curves `4(y+2) = x^(2)` and `4(2-y) =x^(2)` in the region `x in [-2 sqrt(2),2sqrt(2)]`. Then radius of this circle is

Options

A. `sqrt(2)`
B. `sqrt(3)`
C. `(1)/(sqrt(3))`
D. `(3)/(2)`

Answer

A

Explanation

Let the radius of circle is r.
From geometry, `P -= (rsqrt(2),(r )/(sqrt(2)))`.
Now, this point lies on the curve `4(2-y) =x^(2)`
`rArr 4(2-(r )/(sqrt(2))) = (rsqrt(2))^(2)`
`rArr r = sqrt(2)`