Question

Please help :)
You can make a solar hot dog cooker using foil-lined cardboard shaped as a parabolic trough. The drawing at the right shows how to suspend a hot dog with a wire through the focus of each end piece. If the trough is
12 inches wide and 4 inches deep, how far from the bottom should the wire be placed?

Answer 1

well, to be fair, I'd much rather use a stove for that :)

Answer 2

have you covered parabolas yet?

Answer 3

haha for sure. and yes

Answer 4

does \(\begin{array}{llll}
(y-{\color{blue}{ k}})^2=4{\color{purple}{ p}}(x-{\color{brown}{ h}}) \\
(x-{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y-{\color{blue}{ k}})\\
\end{array}

\qquad
\begin{array}{llll}
vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\\
{\color{purple}{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\)

ring a bell?

Answer 5

no, we learned the formulas y^2=4px and x^2=4py

Answer 6

well ahemm \(\begin{array}{llll}
(y-{\color{blue}{ 0}})^2=4{\color{purple}{ p}}(x-{\color{brown}{ 0}})\implies y^2=4px \\
(x-{\color{brown}{ 0}})^2=4{\color{purple}{ p}}(y-{\color{blue}{ 0}})\implies x^2=4py\\
\end{array}\)

so, it's pretty much the same thing, but the one you showed above, it's just when h = 0 and k =0, namely, when the vertex is at the origin

Answer 7

but when the vertex is not at the origin, the one shown above, applies, since it's the general form

anyhow, putting that aside

you're pretty much asked, where the "focus" point for the parabola is at
and the focus point is "p" distance from the vertex
well, let's take a peek at that cooker


so... the "p" distance, is somewhere between 0 and 4 over the y-axis