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>0x = \frac{5}{t} - 7 \quad y = \frac{6t - 2}{4t + 3} \quad t > 0x=t5−7y=4t+36t−2t>0
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>kg(x) = \frac{ax + b}{cx + d} \quad x > kg(x)=cx+dax+bx>k
where a,b,c,d a, b, c, d\,a,b,c,d and k k\,k are integers to be found.
Hence, or otherwise, state the range of ggg.
Practise Edexcel A Level Maths Parametric Equations with exam-style questions for A Level Maths. 64 questions covering 8.1 Parametric Equations, 8.2 Using Trigonometric Identities, 8.3 Curve Sketching, 8.4 Points of Intersection, and 8.5 Modelling with Parametric Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.