1.

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

Answer»

`sqrt(2)`
`sqrt(3)`
`(1)/(sqrt(3))`
`(3)/(2)`

SOLUTION :
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)`


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