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−2t>0Show 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+bx>kwhere 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.
143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.