A concert stage has a parabolic roof. The front edge of the roof is defined by the equation ℎ(?) = −1/8?^2 + 8, where ? is the horizontal distance from the centre and ℎ is the height, both in metres....

A concert stage has a parabolic roof. The front edge of the
roof is defined by the equation ℎ(?) = −1/8?^2 + 8, where ? is
the horizontal distance from the centre and ℎ is the height,
both in metres. A vertical lighting tower is built at ? = 9.
Coloured laser lights are installed at various intervals going
up the tower. The beams of light are to shine on the front
edge of the roof, with their paths defined by the following equations.
Blue: 6? + 8? − 73 = 0 . Green: ? + 2? − 17 = 0
Orange: ? + ? − 10 = 0 . Red: 4? + 8? − 83 = 0

Question: Determine the coordinates of any point(s) of intersection of each laser beam with the edge of the roof. All but one of these laser beams share a common property. Describe the property.