Conversion of parametric function to Cartesian form: x = 1/2(t + (1/t)) y = ...

[Bazoya]

Hi guys, new to this forum. I wonder if you could help me.

I am trying to convert the following parametric function to standard Cartesian form, and experiencing a little difficulty.

x = 1/2(t + (1/t))
y = 1/2(t - (1/t))
1 <= t <= 8

If you could show me the process of achieving this that would be great.
Any help would be appreciated.

Thanks

Jake

 

[Deleted member 4993]

Hi guys, new to this forum. I wonder if you could help me.

I am trying to convert the following parametric function to standard Cartesian form, and experiencing a little difficulty.

x = 1/2(t + (1/t))
y = 1/2(t - (1/t))
1 <= t <= 8

If you could show me the process of achieving this that would be great.
Any help would be appreciated.

Thanks

Jake

What is the expression for x^2?

What is the expression for y^2?

Do you see a way to relate those?

 

[Bazoya]

What is the expression for x^2?

What is the expression for y^2?

Do you see a way to relate those?

Hi, the book I am studying from later gives the answer x^2 - y^2 = 1, which I can find easily enough through substitution and manipulation. What it is that I do not understand is where does the intuition come from to square the expressions in the first place. Is the (t + (1/t)) (t - (1/t)) being a difference of squares the reason?

Also, is the form
x^2 - y^2 = c
a common form of equation and that why it seems logical to try to relate the expressions? I have not yet come across such equation.

Thanks

Jake