Interesting maths question?

A particle moves so that its position vector at time t, t > or equal to 1, is given by

r(t) = (t+1/t)i + (t-1/t)j

Find the Cartesian equation of the path of the particle and state the domain and range.

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

Parametric equations:

x(t) = t + 1/t

y(t) = t – 1/t

Hence:

x+ y = 2t

<=> t = (x+y)/2

Therefore:

x = (x+y)/2 + 2/(x+y)

y = (x+y)/2 – 2/(x+y)

Each equation simplifies to:

x² – y² = 4,

which is equation of a hyperbola.

Since t>=1, the particle moves along the right-hand branch of the hyperbola, starting from the point (2,0) in the “north-eastern” direction.

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