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A point P moves on x-y plane such that P...

A point P moves on x-y plane such that `PS +PS' = 4` where `S(K,0)` and `S'(-K,0),` then which of the following is not true about the locus of P?

A

ellipse if `K in (-2,2)`

B

pair of coincidence lines if `K = +-2`

C

empty if `K in (-oo,-2) uu(2,oo)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
If PSS' forms a triangle, then ellipse
`:. PS + PS' gt SS'`
`rArr K in (-2,2)`
If PSS' is collinear, the pair of coincident lines `rarr K = +-2`
If PSS' neither forms triangle nor collinear then empty set
`rArr PS + PS^(1) lt SS^(1)`
`rArr K in (-oo,-2) uu(2,oo)`
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