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  • Let     be a double ordinate of the parabola,  <img alt="\mathrm {y^2=-4

Let   \mathrm {P Q}  be a double ordinate of the parabola,  \mathrm {y^2=-4 x} , where  \mathrm {P} lies in the second quadrant. If  \mathrm {R} divides  \mathrm {P Q}  in the ratio \mathrm {2: 1} , then the locus of  \mathrm {R} is
 

Option: 1

\mathrm {9 y^2=4 x}


Option: 2

\mathrm {9 y^2=-4 x}


Option: 3

\mathrm {3 y^2=2 x}


Option: 4

\mathrm {3 y^2=-2 x}


Answers (1)

best_answer

Let  \mathrm {P\left(-t_1^2, 2 a t_1\right), Q\left(-t_1^2,-2 t_1\right)} and  \mathrm {R(h, k)} 
\begin{aligned} & \Rightarrow h=-t_1^2, k=\frac{-2 t_1}{3} \\ & \Rightarrow 9 k^2=-4 h \Rightarrow 9 y^2=-4 x \end{aligned}  is required equation of locus. 

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Rishabh

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