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Let P be the point (-3,0) and Q be a mov...

Let P be the point `(-3,0)` and Q be a moving point (0,3t). Let PQ be trisected at R so that R is nearer to Q. RN is drawn perpendicular to PQ meeting the x-axis at N. The locus of the mid-point of RN is

A

`(x+3)^(2)-3y = 0`

B

`(y+3)^(2)-3x = 0`

C

`x^(2)-y = 1`

D

`y^(2)-x = 1`

Text Solution

Verified by Experts

The correct Answer is:
D

`P(-3,0), Q(0,3t), R(-1,2t)`
Let the mid point of RN be (h,k)
`:. k = t`.
`RN _|_ PQ rArr (2t)/(-2h-2) xx (3t)/(3) =-1`
`rArr 2t^(2)=2h +2`
`rArr t^(2)=h+1`
`rArr k^(2)=h +1`
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