A few days ago
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
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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