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Question

Pls answer my ques..
What is the locus of a variable point P(t + 1/t, t - 1/t)??

Answer 1

It's a hyperbola, with cartesian equation x^2 - y^2 = 4.

To obtain this, set x = t + 1/t and y = t - 1/t. Add and subtract the two equations to get that

x + y = 2t and x - y = 2/t.

Now you can solve both equations for t and equate them to each other. This results in the above equation, which is a hyperbola with vertices at (2,0) and (-2,0), and y = +/- x as asymptotes.

Answer 2

x = t + 1/t
y = t - 1/t

Observe that x² - y² = 4. This is the equation for a hyperbola.
Which part of it is traced out by P depends on the range for the parameter t.

Answer 3

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