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Well, you can attempt in the ways below by trying to eliminate the existence of "t" in two equations and combine them into one:


1) x = t^2 - 2t and y = t^2 + 2

Hence, x = ( y - 2 ) - 2t

( x - y + 2 ) = -2t

( x - y + 2 )^2 = 4t^2 = 4( y - 2 )

[ ( x - y ) + 2 ]^2 = 4( y - 2 )

( x - y )^2 + 4( x - y ) + 4 = 4y - 8

( x - y )^2 + 4( x - 2y ) + 12 = 0

( y - x )^2 - 4( 2y - x ) + 12 = 0
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2) x = 3( t + 1/t )

x^2 = 9( t^2 + 2 + 1/t^2 )

y = 4( t - 1/t )

y^2 = 16( t^2 - 2 + 1/t^2 )

Solve by elimination method:

16 x^2 - 9 y^2

= 144 ( t^2 + 2 + 1/t^2 ) - 144 ( t^2 - 2 + 1/t^2 )

= 576

Hence, divide both sides by 576, we have

x^2/36 - y^2 / 64 = 1
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Hope I can help you.