1. ## Parabola Searchlight

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the depth of the searchlight is 4 feet, what should the width of the opening be?

2. Hello, magentarita!

A searchlight is shaped like a paraboloid of revolution.
The light source is located 2 feet from the base along the axis of symmetry
and the depth of the searchlight is 4 feet.
What should the width of the opening be?
Code:
                   4|
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*          |          *
*        2*         *
*       |       *
*    |    *
- - - - - - - * - - - - - - -
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We are expected to know this equation: . $x^2 \:=\:4py$
. . where $p$ is the distance from the focus to the vertex.

Since $p = 2$, the equation is: . $x^2 \:=\:8y$

When $y = 4\!:\;\;x^2 \:=\:32\quad\Rightarrow\quad x \:=\:\pm4\sqrt{2}$

Therefore, the width of the opening is $8\sqrt{2}$ feet.

3. ## ok....

Originally Posted by Soroban
Hello, magentarita!

Code:
                   4|
* - - - - - + - - - - - *
|
*          |          *
*        2*         *
*       |       *
*    |    *
- - - - - - - * - - - - - - -
|
We are expected to know this equation: . $x^2 \:=\:4py$
. . where $p$ is the distance from the focus to the vertex.

Since $p = 2$, the equation is: . $x^2 \:=\:8y$

When $y = 4\!:\;\;x^2 \:=\:32\quad\Rightarrow\quad x \:=\:\pm4\sqrt{2}$

Therefore, the width of the opening is $8\sqrt{2}$ feet.
Another great reply. How did you know what equation to use to solve this question?

4. Originally Posted by magentarita
Another great reply. How did you know what equation to use to solve this question?
An equation of a parabola with vertex at the origin and a vertical axis of symmetry is:

$x^2=4py$ where p is the distance from the focus to the vertex.

See here.

5. ## ok but.....

Originally Posted by masters
An equation of a parabola with vertex at the origin and a vertical axis of symmetry is:

$x^2=4py$ where p is the distance from the focus to the vertex.

See here.
Ok but I still would like to know how Soroban makes those pictures.

6. Originally Posted by magentarita
Ok but I still would like to know how Soroban makes those pictures.
I won't attempt to speak for Soroban, but I think he just uses the symbols on his keyboard to draw the objects and then puts "code" tags around it to preserve the spacing. I guess he just highlights his drawing and selects the # symbol at the top of the edit screen to put the tags on. That's how I do it when I want to make a table or something.