Question

An engineer designs a satellite dish with a parabolic cross section. The dish is 5m wide at the opening, and the focus is placed 1.2m from the vertex 

(a) Position a coordinate system with the origin at the vertex and the x-axis on the parabola’s axis of symmetry and find an equation of the parabola. 

(b) Find the depth of the satellite dish at the vertex.

Answer 1

From the diagram,

(a) Consider the satellite dish is open rightward parabola 

y² = 4 ax … (1) 

Clearly a = 1.2m 

(1) ⇒ y² = 4(1.2) 

y² = 4.8x

(b) Use the point (x₁, 2.5) in (1) 

(2.5)² = 4(1.2)x₁ 

(2.5)²/4(1.2) = y₁ 

x₁ = 1.3 m 

∴ The depth of the satellite dish at vertex is 1.3 m