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A point moves so that its distance from ...

A point moves so that its distance from the point `(2,0)` is always `(1)/(3)` of its distances from the line `y=x-18`. If the locus of the points is a conic, then length of its latus rectum is

A

`(16)/(3)`

B

`(32)/(3)`

C

`(8)/(3)`

D

`(15)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly, locus is ellipse with eccetntircity `e=(1)/(3)`.
Hence, focus is (2,0) and directrixd is x-18=0
Distance of focus from directrix=16
`rArra//e-ae=16`
`:.(8)/(3)a=16`
`:.a=6`
`:. b^(2)=a^(2)(1-e^(2))=36(1-1//9)=32`
`:. L.R.=(2b^(2))/(A)=(32)/(3)`
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