Q11. - Algebra 2

Question

COMMUNICATION A microphone is placed at the focus of a parabolic reflector to collect sound for the television broadcast of a World Cup soccer game. Write an equation for the cross section, assuming that the focus is at the origin and the parabola opens to the right.

Step-by-Step Solution

Answer

The equation of the cross section is $x=6y^2-6$.

Step 1. Given

A microphone is placed at the focus of a parabolic reflector to collect sound for the television broadcast of a World Cup soccer game.

Step 2. To determine

Write an equation for the cross section, assuming that the focus is at the origin and the parabola opens to the right.

Step 3. Calculation

The focus is at the origin. And the vertex is 6 units to the left from (0, 0). 

So, the vertex is $(h,k)=(-6,0)$.

The distance between the vertex and the focus is = a = 6.

So, the equation of the cross section is:

$\begin{array}{l}x=a{\left(y-k\right)}^2+h\\ x=6{\left(y-0\right)}^2+\left(-6\right)\\ x=6y^2-6\end{array}$