Question

State the coordinates of the focus and the directrix equation for each parabola. *Show work and explain how you got what you got*

Answer 1

\[x = \frac{ 1 }{ 20 } (y - 1)^2 - 4\]

Answer 2

vertex is pretty clear right?

Answer 3

yea (-4, 1)

Answer 4

and the AOS = y = 1 right

Answer 5

yeah that looks good

Answer 6

and you know which way it faces right?

Answer 7

not sure what you mean by "horizonal"
since the y is squared it opens to the right or left, and since \(\frac{1}{20}\) is positive if opens to the right

Answer 8

How do you find the focus and directrix?

Answer 9

it is easier if we write it as
\[20(x+4)=(y-1)^2\] then we see that it looks like
\[4p(x-h)=(y-k)^2\] making \(4p=20\) and so \(p=5\)
then we can find the focus and the directrix easily

Answer 10

Well I did it this way: \[\frac{ 1 }{ 4(\frac{ 1 }{ 20 }) } = 5\]

Answer 11

ok that works too

Answer 12

that's the way we use it in class

Answer 13

so you know \(p=5\) and that makes the focus 5 units to the right of \((-4,1)\) and the directrix 5 units to the left

Answer 14

that is why you have to know which way it is oriented, to know whether to go up and down or left and right

Answer 15

do we mess with the x or y coordinate

Answer 16

since it is right and left, mess with the x's

Answer 17

I know you would add 5 to -4 <---- from vertex to get a focus of (1,1)

Answer 18

yup

Answer 19

then you would subtract -4 - 5 to get -9; which is the directrix

Answer 20

the dirextix is a line, namely \(x=-9\) but yeah essentially

Answer 21

okay so thanks for the help; we just got introduced to this today so I was kind of iffy on it

Answer 22

looks like you got a decent handle on it
yw