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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.

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.

Grade:11

2 Answers

Vijay Mukati
askIITians Faculty 2590 Points
5 years ago
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 t2.You will get the locus of R.

Thanks,
Ankit Jaiswal
165 Points
5 years ago
 

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 t2.You will get the locus of R.
 

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