A straight walking path in a public park is modelled by the equation 2y=3x+4 and passes through the point (2,5). A new jogging track has to run parallel to this path and must pass through the park gate located at (−6,9).
(i) Determine the equation of the jogging track.
(ii) Find the exact points where the jogging track meets the x-axis and the y-axis.
(iii) Calculate the length of the segment of the jogging track intercepted between the coordinate axes.