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A variable point P is on the circle x^2 ...

A variable point `P` is on the circle `x^2 + y^2 =1` on xy plane. From point P, perpendicular PN is drawn to the line `x =y =z` then the minimum length of PN is:-

A

`sqrt(2)`

B

`1/sqrt(2)`

C

`sqrt(3)`

D

`1/sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Any point on the circle `x^(2)+y^(2)=1` is
`P(costheta,sintheta,0)`
Distance of P from O(0,0,0) which lies on the line x =y=z is OP=1
1,1,1 is
`d=(costheta+sintheta)/sqrt(3)`
`therefore PN = sqrt(1-(costheta+sintheta)/sqrt(3))^(2)`
`=sqrt(2-sin2theta)/sqrt(3)`
`therefore PN_("min") = sqrt((2-1)/3) = sqrt(1/3)`
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