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1.5.14 Convert between cartesian and parametric forms (A-level only)

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Question 41

The spatial coordinates (x,y)(x, y)(x,y) of a particle moving through a controlled force field are defined by the parametric equations

x=5t−7y=6t−24t+3t>0 x = \frac{5}{t} - 7 \quad y = \frac{6t - 2}{4t + 3} \quad t > 0 x=t5​−7y=4t+36t−2​t>0
a.

Show that the equation of the trajectory can be written in the form y=g(x)y = g(x)y=g(x) where g g\,g is the function

g(x)=ax+bcx+dx>k g(x) = \frac{ax + b}{cx + d} \quad x > k g(x)=cx+dax+b​x>k

where a,b,c,d a, b, c, d\,a,b,c,d and k k\,k are integers to be found.

[5]
b.

Hence, or otherwise, state the range of ggg.

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1.5.14 Convert between cartesian and parametric forms (A-level only) Questions

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