# Let PQ be a double ordinate of the parabola, where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1, then the locus of R is : Option 1) Option 2) Option 3) Option 4)

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)

Incorrect option

Option 2)

Correct option

Option 3)

Incorrect option

Option 4)

Incorrect option

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