Geometry of the Parabola help, eliminating the paramter (1 Viewer)

[Jackson94]

Eliminate the parameter and hence find the Cartesian equation of the curve.
x=t + 1/t, y=t^2 + 1/t^2

 

[xXnukerrrXx]

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

similarly to the property a^2+b^2=(a+b)^2-2ab
(1) x^2=(t+(1/t))^2=t^2+(1/t^2)+2
therefore to get t^2+(1/t^2) we minus the 2
x^2-2=t^2+(1/t^2)
substitute t^2+(1/t^2) in equation (2)
y=x^2-2

 

[Jackson94]

Thank you very much!