Author Topic: im so stupid :( (Read 574 times) Tweet Share

babyface · « **on:** April 26, 2014, 01:48:03 pm »

i don't underestand q 2b) how do i prove it:

Thank you

Conic · « **Reply #1 on:** April 26, 2014, 02:06:51 pm »

The gradients of QP and RP are the same, since they lie on the same straight line. We can find the gradients using rise/run and equate them:

$\frac{2at}{at^2-a}=\frac{2at-2as}{at^2-as^2}$

$\implies \frac{2t}{t^2-1}=\frac{2t-2s}{t^2-s^2}$ (cancelled the as)

$\implies \frac{2t}{t^2-1}=\frac{2t-2s}{(t+s)(t-s)}$ (difference of two squares)

$\implies \frac{2t}{t^2-1}=\frac{2}{t+s}$ (taking out factor of t-s)

$\implies \frac{t}{t^2-1}=\frac{1}{t+s}$

$\implies t (t+s)= (t^2-1)$ (cross multiply)

$\implies t^2+st= t^2-1$

$\implies st=-1$

$\implies s=\frac{-1}{t}$

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Author Topic: im so stupid :( (Read 574 times) Tweet Share

babyface

im so stupid :(

Conic

Re: im so stupid :(

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