P is the point (2ap,ap^2) on the parabola x^2=4ay. The tangent at P meets the axis of the parabola at T and PN is drawn perpendicular to the axis, meeting it at N. The directrix meets the axis at A.

(a) Prove OS=OA

Question

P is the point (2ap,ap^2) on the parabola x^2=4ay. The tangent at P meets the axis of the parabola at T and PN is drawn perpendicular to the axis, meeting it at N. The directrix meets the axis at A.

(a) Prove OS=OA

anonymous · Answer

where is point S?

mimi_x3 · Answer

Um, idk, I think S is the focal length

anonymous · Answer

the definition of the parabola is that the distance between the point P with the focus S is equal to the distance from the point P to the linear directrix.
OS=OA is the special situation when P is point O.

anonymous · Answer

Is this what it asks?

mimi_x3 · Answer

idk, i don't understand the question, i just don't understand parametrics xD

mimi_x3 · Answer

Can you help ?

anonymous · Answer

I don't know what the question is asking for.

anonymous · Answer

You must provide more details.

mimi_x3 · Answer

Oh yeah I forgot sorry
a) Prove (i) OS=OA (O is vertex, S is the focus)

anonymous · Answer

then i have typed the answer:
the definition of the parabola is that the distance between the point P with the focus S is equal to the distance from the point P to the linear directrix.
OS=OA is the special situation when P is point O since point O is on the parabola.

mimi_x3 · Answer

Don't you have to solve it or something to prove that OS=OA like finding the equation of tangent

anonymous · Answer

for the question a) OS=OA, I don't think so.

anonymous · Answer

i think you will use it when you are going to solve other questions

mimi_x3 · Answer

Okay, I will draw the diagram that I drew can you check if its correct ?

anonymous · Answer

no problem.

mimi_x3 · Answer

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