The lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex form A. HP B. GP C. AP Answer is GP

Question

Aditya Gupta · Answer

consider a parabola y^2=4ax; a>0, with focus (a,0) and tangent to the vertex being x=0 now, let a focal chord intersect the parabola at (at^2, 2at) and (ap^2, 2ap) as this chord passes thru focus, we have [2ap-2at]/[ap^2-at^2]=2ap/[ap^2-a] or pt= –1 or p^2t^2=1 now, the lengths from the tangent at vertex are: at^2, a, ap^2 we see that a/at^2=ap^2/a so, the lengths are in GP

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The lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex form A. HP B. GP C. AP Answer is GP

The lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex form
A. HP
B. GP
C. AP

Answer is GP

1 Answers

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The lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex form A. HP B. GP C. AP Answer is GP

The lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex formA. HPB. GPC. AP Answer is GP

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The lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex form
A. HP
B. GP
C. AP

Answer is GP