Question

Work the item as directed.

Type the equation of the directrix and state the coordinates of the focus points for x = y2/12.

F = (, )

Directrix is x =

Answer 1

Since now one knows how to do this I need help with this...Solve this problem using two variables. One number is 2 times another number plus 3. Their sum is 21. Find the numbers.

Answer 2

for a parabola of that kind, the "focus form" will be \(\bf (y-k)^2=4p(x-h)\)

vertex is at the coordinates of (h, k)
p = distance from the vertex to the focus point

since what you have is \(\bf x = \cfrac{y^2}{12}\implies 12x =y^2\implies 12(x-0)=(y-0)^2\)


can you see where the vertex is at?

Answer 3

Lol... I JUST figured it out like 2 minutes ago. it's 0,0 1/4...right?

Answer 4

the vertex is at (0,0), yes
the focus is at \(\bf 4p = 12 \implies p = \cfrac{12}{4}\)

Answer 5

So 3?

Answer 6

so p =3

keep in mind that the parabola has a squared "y" variable, meaning is opening sideways, "p" is positive that means, the parabola is opening towards the left-hand-side

so the focus point is at (3 , 0)

the Directrix is EXACTLY the same distance from the vertex, "3", but in the opposite direction of the vertex, so the the line crosses at (-3, 0) thus x = -3

Answer 7

So it's (0,0) and p=3?

Answer 8

Or is it3,0

Answer 9

yeap, because the parabola has a \(\bf y^2\) component, and thus it's opening sideways, P is positive, thus from left to right

Answer 10

say we have 2 numbers, "a" and "b"

" One number is 2 times another number"
\(\bf a = 2b\)
"plus 3"
\(\bf a = 2b +3\)

"Their sum is 21"

\(\bf a + b = 21\)

we know \(\bf a = \color{red}{2b+3}\)
so we could say that

\(\bf (\color{red}{2b + 3}) + b = 21\)

solve for "b" to find "b"
once you find "b", to get "a", well, recall that a = 2b + 3

Answer 11

There answer is 15 and 6

Answer 12

Sorry

Answer 13

I did it before I saw your post.

Answer 14

good :)

Answer 15

15 and 6 are correct

Answer 16

I'm still confused about the other answer... it's 3,0...3. A yes or no will do.

Answer 17

hmm... the focus point is a point, an x-coordinate and a y-coordinate, in the "focus form" of the parabola \(\bf (y-k)^2=4p(x-h)\) P = distance from the vertex to either one

if P = 3, that is, the distance from the vertex to the focus is 3, then the focus is at (3, 0)
that is, if you move horizontally from (0, 0) over the x-axis, 3 units to the right, you'd end up at ( 3, 0)


the Directrix is just a line, if you move from the vertex (0, 0), in the opposite direction, to the left 3 units, you'd end up at (-3, 0) but the Directrix is just a line, not a ordered pair point, so the line equation is x = -3

Answer 18

Ummm thanks?

Answer 19

still confused?

Answer 20

anyhow... yw :)