+25 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 24 inches wide and 4 inches deep, how far from the vertex should the microphone be placed?
+128406 Let the vertex be at (0,0)
And the point (12, 4) is on the parabola.....so we have the form
y = mx^2 and we know that
4 = m(12)^2
4 = 144m divide both sides by 144
1/36 = m
So.....the form is
y = (1/36)x^2
36y = x^2
And 36 = 4a divide both sides by 4
9 = a
So...the focus is given by (0, 0 +a) = (0, 0 + 9) = (0, 9)
So.....the microphone should be placed 9 inches from the vertex
