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Discussion Response Post to: parabola

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13 Feb 2008 20:35:00 IST

Subject: Re:parabola

raulrag009 (1223)

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Consider the parabola y²=4ax

Let PQ be latus rectum

Let AB be a focal chord

Let FB=c₁ FA=c₂

Let the coordinates of A and B be (at₁²,2at₁) and (a/t₁² , -2a/t₁)

As t₁t₂=-1

F=(a,0)

NOW

c₁=a[1+t₁²]/t₁² and c₂ = a[1+t₁²]

c₁+c₂ = a[1+t₁²]/t₁² + a[1+t₁²]

c₁c₂ =a²/t₁² [1+t₁²]²

divide both

c₁c₂/c₁ +c₂ = a

multiply by 2 on both sides

2c₁c₂/c₁+c₂ =2a

thus

proved

this reply: 5 points (with 1 Olaaa!! Perrrfect answer.

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