91Ó°ÊÓ

Parabolic car headlights: The cross section of a typical car headlight can be modeled by an equation similar to \(25 x=16 y^{2},\) where \(x\) and \(y\) are in inches and \(x \in[0,4] .\) Use this information to graph the relation for the indicated domain.

The natural draft cooling towers for nuclear power stations are called hyperboloids of one sheet. The perpendicular cross sections of these hyperboloids form two branches of a hyperbola. Suppose the central cross section of one such tower is modeled by the hyperbola \(1600 x^{2}-400(y-50)^{2}=640,000 .\) What is the minimum distance between the sides of the tower? Assume \(x\) and \(y\) are in feet.

The reflector of an industrial spot light has the shape of a parabolic dish with a diameter of \(120 \mathrm{cm} .\) What is the depth of the dish if the correct placement of the bulb is \(11.25 \mathrm{cm}\) above the vertex (the lowest point of the dish)? What equation will the engineers and technicians use for the manufacture of the dish? (Hint: Analyze the information using a coordinate system.)