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

A concert stage has a parabolic roof. The front edge of theroof is defined by the equation ℎ(?) = −1/8?^2 + 8, where ? isthe 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 goingup the tower. The beams of light are to shine on the frontedge 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: Consider the one laser light that does not share the common property. Keeping the location of the light source fixed, determine a new equation for the path of the laser light so that it now shares the common property. Where does it intersect the edge of the roof?