Answer: 9 inches.
Step-by-step explanation:
Given: The width of the parabola= 24 inches
The depth of the parabola = 4 inches
Assume the parabola open upwards and the vertex of the parabola be (0,0)
Then the point on parabola (x,y)=\((-\frac{24}{2},4)\ and (+\frac{24}{2},4)\)
⇒ (-12,4) and (12,4) are points on parabola.
Equation of parabola opens upwards with vertex=(0,0) is \(x^2=4ay\)
Put (12,4) in the equation, we get
\((12)^2=4a(4)\\\Rightarrow\ 144=16a\\\Rightarrow\ a=\frac{144}{16}=9\\\Rightarrow\ a=9\)
Since, the microphone itself is placed on the focus of the parabola.
Hence, the microphone is 9 inches far from the vertex.
