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March 28, 2024, 07:46:44 pm

Author Topic: Re: Parametric, Cambridge Ext 1, Exercise 9E Q12  (Read 1006 times)  Share 

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24221

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Re: Parametric, Cambridge Ext 1, Exercise 9E Q12
« on: August 06, 2018, 11:25:48 am »
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A focal chord AB of a parabola meets the directrix at D. Prove the focus S divides AB internally in the ratio k:1. Then D divides AB externally in the ratio k:1

Thank you, :D

RuiAce

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Re: Re: Parametric, Cambridge Ext 1, Exercise 9E Q12
« Reply #1 on: August 07, 2018, 09:29:57 am »
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A focal chord AB of a parabola meets the directrix at D. Prove that if focus S divides AB internally in the ratio k:1. Then D divides AB externally in the ratio k:1

Thank you, :D
I was able to retrace the question with thanks to the textbook reference. In the future please be cautious of typos because not everyone will have the textbook and thus the question won't make any sense to them.

Remark: One may show that \(D\) is the point \( \left( \frac{4a}{p^{-1} - p}, -a \right) \), but we only really care about the \(y\)-coordinate here.

One may check that \(k=p^2\) actually works by testing it out with the corresponding \(y\)-coordinates as well.
« Last Edit: August 07, 2018, 09:33:59 am by RuiAce »

24221

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Re: Parametric, Cambridge Ext 1, Exercise 9E Q12
« Reply #2 on: August 07, 2018, 07:35:12 pm »
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Thank you very much, this helped out a lot!