Maximum illumination will be achieved if the bulb is placed at the focus of the parabola created by the cross-section of the headlight.
If we rearrange the equation we know that:
`x=1/15y^2` , therefore, a = 1/15
The focus of a parabola is located at:
If we place the vertex of the parabola at the origin (0,0) for simplicity this gives:
Substituting our known value of a we get:
Therefore, the bulb should be placed 3.75 units to the right of the vertex.