A concert stage has a parabolic roof. The front edge of theroof is defined by the equation h(x) = −1/8x^2 + 8, where x 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(x) = −1/8x^2 + 8, where x isthe horizontal distance from the centre and h is the height,both in metres. A vertical lighting tower is built at x = 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: 6x + 8y − 73 = 0 . Green: x + 2y − 17 = 0. Orange: x + y − 10 = 0 . Red: 4x + 8y − 83 = 0

Question: Determine an equation for the path of a fifth purple laser beam that is to touch the edge of the roof at its vertex. How high on the tower would this light source be located?