Let P be a point on the parabola y 2 -2y-4x+5=0, such that the tangent on the parabola at P intersects the directrix at point Q. let R be the point that divides the line segment QP externally in the ratio ½ : 1 . Find the locus of R.

Question

Let P be a point on the parabola y 2 -2y-4x+5=0, such that the tangent on the parabola at P intersects the directrix at point Q. let R be the point that divides the line segment QP externally in the ratio ½ : 1 . Find the locus of R.

Vikas TU · Answer

Dear Student,

vertex of parabola = 1,1

Directrix = x=0

Eq of parabola : (y-1)^2 = 4(x-1) ; a=1

P= (t^2,2t)

Q=(0,t)

R= ( 2t^2, 3t)

For point R, x=2t^2 ; y= 3t

Eliminating t from the two equations, we get 9x= 2y^2 as the locus of R

Cheers!!

Regards,

Vikas (B. Tech. 4^th year
Thapar University)

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Let P be a point on the parabola y 2 -2y-4x+5=0, such that the tangent on the parabola at P intersects the directrix at point Q. let R be the point that divides the line segment QP externally in the ratio ½ : 1 . Find the locus of R.

Let P be a point on the parabola y²-2y-4x+5=0, such that the tangent on the parabola at P intersects the directrix at point Q. let R be the point that divides the line segment QP externally in the ratio ½ : 1 . Find the locus of R.

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Let P be a point on the parabola y 2 -2y-4x+5=0, such that the tangent on the parabola at P intersects the directrix at point Q. let R be the point that divides the line segment QP externally in the ratio ½ : 1 . Find the locus of R.

Let P be a point on the parabola y2 -2y-4x+5=0, such that the tangent on the parabola at P intersects the directrix at point Q. let R be the point that divides the line segment QP externally in the ratio ½ : 1 . Find the locus of R.

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Let P be a point on the parabola y²-2y-4x+5=0, such that the tangent on the parabola at P intersects the directrix at point Q. let R be the point that divides the line segment QP externally in the ratio ½ : 1 . Find the locus of R.