SOLUTION: A field microphone used at a soccer game has a parabolic cross section and is 26 in. wide at the opening. The focus is 25 in. from the vertex. Find the depth of the microphone

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A field microphone used at a soccer game has a parabolic cross section and is 26 in. wide at the opening. The focus is 25 in. from the vertex. Find the depth of the microphone      Log On


   

Question 744053: A field microphone used at a soccer game has a parabolic cross section and is 26 in. wide at the opening. The focus is 25 in. from the vertex. Find the depth of the microphone
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Derivation for a simple equation of a parabola gives 4py=x%5E2, where p is the distance from the focus to the vertex. You can represent your given parabola as a graph with vertex at (0,0) and focus would be at (0,25). The simple equation from the derivation can be arranged as y=%281%2F%284p%29%29x%5E2. Knowing p=25, you have highlight%28y=%281%2F100%29x%5E2%29.

You are asked about the depth given that the widest part has a cross section 26 inches, meaning the diameter is 26 inches, meaning radius, distance from the axis of symmetry, is 13 inches. This depth corresponds to the value of y when x=13.

y=%281%2F100%29%2A13%5E2=169%2F100=highlight%281.7%29 inches, rounded to two figures based on the accuracy used in the description. Theoretically 1.69 inches.