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The eccentricity of the locus of point (...

The eccentricity of the locus of point `(3h+2,k),` where `(h , k)` lies on the circle `x^2+y^2=1` , is

A

`1//3`

B

`sqrt(2)//3`

C

`2sqrt(2)//3`

D

`1//sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
(1) Let p =3h+2 and q=k
or `h=(p-2)/(3) and k=q`
Since (h,k) lies on `x^(2)+y^(2)=1`
`h^(2)+k^(2)=1`
or `((p-2)/(3))^(2)+q^(2)=1`
The locus is
(2) `((x-2)/(3))^(2)+y^(2)=1`
which has eccentricity
`e=sqrt(1-(1)/(9))=(2sqrt(2))/(3)`
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