Gabriella is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by (y+3)^2=26(x-2) where x and y are measured in inches. Where should she place the bulb to ensure a perfect beam of light?
Accepted Solution
A:
the bulb should be placed at the "focus point" of the parabolic mirror.
[tex]\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}})
\end{array}
\qquad
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\[/tex]
bear in mind that, because the leading term's coefficient is positive, namely for yΒ², the parabola opens to the right, and "p" is positive, therefore the focus point will be to the right of the vertex.