question_answer

Let PQ be a double ordinate of the parabola, \[{{y}^{2}}=-4x,\]where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1, then the locus of R is : [JEE Main Online Paper (Held On 11 April 2015)]  

A)  \[9{{y}^{2}}=4x\]

B)  \[9{{y}^{2}}=-4x\]

C) \[3{{y}^{2}}=2x\]

D) \[3{{y}^{2}}=-2x\]

Correct Answer: B

Solution :

  End points of double ordinate can be taken as \[\left( -{{t}^{2}},2t \right)\And \left( -{{t}^{2}},-2t \right)\] according to given condition. \[x=\frac{-2{{t}^{2}}-{{t}^{2}}}{3}\And y=\frac{-4t+2t}{3}\] \[\Rightarrow \]\[3x=-3{{t}^{2}}\And 3y=-2t\] i.e., \[x=-{{t}^{2}}\And t=-{}^{3}/{}_{2}y\]eliminatry t \[x=-{{\left( -\frac{3y}{2} \right)}^{2}}\]i.e., \[x=-\frac{9}{4}{{y}^{2}}\]i.e., \[9{{y}^{2}}=-4x\]