Question

The parabola graphed below represents a side view of a parabolic microphone dish. The directrix is drawn in as well. The end of the microphone is placed on a feedhorn that will need to be placed at the focus of the parabola to pick up the sound. The scale of the graph is in inches.



Based on the graph, the engineers should make the feedhorn _____ inches long.(image attached)

Answer 1

@amistre64

Answer 2

In this question, you'd first have to find the focus. How would you go about doing that, already knowing the directrix?
Then, you look at the distance between the vertex of the parabola and its focus. That distance should give you the length of the feedhorn.

Answer 3

I legit do not know this is so different from the problems the teacher taught me. I'm only in 11th grade. is this advanced?

Answer 4

I'm not sure where you're from but in Australia this is definitely year 11 material.

Anyway, to give you a start, the directrix is the line x = 4, right?

Answer 5

yes, that's the straight line correct?

Answer 6

Yep. So, what do we know is the relationship between between the directrix and the focus?

Answer 7

they are parallel? and sorry my pc just like freaked out

Answer 8

That's alright. So no, the focus isn't a line (good guess though).
The directrix is a line on one side of the parabola and the focus is a point on the other side.
Their relationship is that, for any point on the parabola, the directrix and the focus are the same distance from that point.

Answer 9

@Tommynaut

Answer 10

And another thing about the focus is that, if you drew a line perpendicular to the directrix that ran through the vertex of the parabola, the focus would lie on that line

Answer 11

so it would reflect over the porabola? sort of

Answer 12

Yeah, sort of. But remember, the focus is just a point.

Answer 13

and it would be on the x axis?

Answer 14

Yep!

Answer 15

So, the vertex is at (0,0) right? How many inches away is the directrix?

Answer 16

4

Answer 17

Awesome. So many how inches away from the vertex (but in the other direction) would the focus be?

Answer 18

4

Answer 19

@Tommynaut

Answer 20

Yes, exactly. So what does that tell us then?

Answer 21

4 would be the answer?

Answer 22

Yep, 4 inches. Can you visualise why that's the case?

Answer 23

yes! oh my gosh that was so flipping easy I can't believe I have been stuck on that. can you help me with another question by chance?

Answer 24

Sure thing, but maybe post it as a new question

Answer 25

okay thank you so much!

Answer 26

No problem :)