two perpendicular chords are drawn from the origin 'O' to the parabola y = x^2, which meet the parabola at P and Q. Rectangle POQR is completed. Find the locus of vertex R.

Dear Student,
Assume P (2at₁², at₁²) and Q (2at₂², at₂²) where a = ¼.
And also assume R (h,k).
Since PO and QO are perpendicular to each other, so by applying this condition, you will get t₁t₂ = -1.
Now use the property of rectangle, that diagonls bisect each other. solve these two equation and eliminate t₁ and t_2.You will get the locus of R.

Thanks,