Question

The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 40 inches wide and 20 inches deep, how far from the vertex should the microphone be placed?

Answer 1

I know that \((\pm20,20\) is one of the points on the parabola just not sure where do I go from there

Answer 2

If we place the vertex at (0,0) we have an equation of the form y=ax^2 so if we plug in the values x=20 and y=20 we can work out a

Answer 3

The focus will be at (0,1/4a)