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.
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.