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
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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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CENGAGE-COORDINATE SYSTEM-Multiple Correct Answers Type
