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 :

 

  • Option 1)

    9y^{2}=4x

  • Option 2)

    9y^{2}=-4x

  • Option 3)

    3y^{2}=2x

  • Option 4)

    3y^{2}=-2x

 

Answers (1)

As learnt in Concept

Double ordinate -

The chord of parabola perpendicular to the axis of symmetry.

-

 

 

Locus -

Locus of a point at a constant distance from a fixed point is a circle.

- wherein

 

 

y^{2}=-4x

Coordinates of R

\left ( \frac{2at^{2}+at^{2}}{3}, \frac{2at-4at}{3} \right )

=> \left ( at^{2},\frac{-2at}{3} \right )

 Now \:h=at^{2}; k=\frac{-2at}{3}

Eliminating t

we get  9k^{2}=-4h

=> 9y^{2}=-4x


Option 1)

9y^{2}=4x

Incorrect option    

Option 2)

9y^{2}=-4x

Correct option

Option 3)

3y^{2}=2x

Incorrect option    

Option 4)

3y^{2}=-2x

Incorrect option    

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