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 November 22nd, 2013, 06:56 PM #1 Newbie   Joined: Oct 2013 Posts: 17 Thanks: 0 Elimination Technique Hey Im stuck on this one question. Eliminate t to give an equation that relates x and y: x=tan(9) , y=sec^2(t)-2 y=_________________ My answer I got after combining the 2 formulas was y=x^2-2, but its wrong...so im sort of stuck here now. Any help appreciated!
 November 22nd, 2013, 07:28 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: Elimination Technique y = sec˛(t) - 2 = tan˛(t) + 1 - 2 = x˛ - 1.
 November 22nd, 2013, 07:38 PM #3 Newbie   Joined: Oct 2013 Posts: 17 Thanks: 0 Re: Elimination Technique OHH thanks!!!
November 23rd, 2013, 03:07 AM   #4
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Re: Elimination Technique

Hello, SamFe!

A slightly different approach . . .

Quote:
 $\text{Eliminate }t: \;\begin{Bmatrix}x\:=\:\tan t \\ \\ \\ y\:=\:\sec^2t\,-\,2 \end{Bmatrix}$

$\text{We have: }\:\begin{Bmatrix} y\,+\,2=&\sec^2t \\ \\ \\ x^2=&\tan^2t \end{Bmatrix}=$

$\text{Subtract: }\:y\,+\,2\,-\,x^2 \;=\;\underbrace{\,\sec^2t\,-\,\tan^2t\,}_{\text{This is 1}}$

$\text{Therefore: }\:y\,+\,2\,-\,x^2 \:=\:1 \;\;\;\Rightarrow\;\;\;y \:=\:x^2\,-\,1$

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