### Instruction: For real numbers $t \neq 0,$ the point
\[(x,y) = \left( t + \frac{1}{t}, t - \frac{1}{t} \right)\]is plotted.  All the plotted points lie on what kind of curve?

(A) Line
(B) Circle
(C) Parabola
(D) Ellipse
(E) Hyperbola

Enter the letter of the correct option.### Response: I want to find out what kind of curve the points $(x,y)$ lie on, so I need to eliminate the parameter $t$ and get a relation between $x$ and $y$.
One way to do that is to use the fact that $(t + \frac{1}{t})^2 - (t - \frac{1}{t})^2 = 4$ for any nonzero $t$.
This means that $x^2 - y^2 = 4$, which is the equation of a hyperbola.
Therefore, the correct option is (E).