Question

Find the vertex, focus, directrix, and focal width of the parabola.

x = 4y^2

Answer 1

The general form of your parabola is $$ \Large x = \frac {1}{4p} y^2 $$Focal width is 4p

Answer 2

ok what do i do wuth that formula

Answer 3

we need to solve 1/(4p) = 4

Answer 4

oh so p = 1/16?

Answer 5

yes

Answer 6

the vertex is (h,k)
directrix is x = -p
focal width is 4p

Answer 7

it is centered at the origin

Answer 8

how do we find h and k

Answer 9

ok the focal width is .25

Answer 10

The general form of a parabola that opens to the right or left \[ \Large x-h = \frac {1}{4p} (y-k)^2 \]Vertex is (h,k)
directrix is x =h -p
focal width is 4p

Answer 11

yes that is correct

Answer 12

is the focal width represented as a single letter?

Answer 13

4 times that value of p

Answer 14

like i know i can plug in x as 4y^2 but thats still not enough to find either h or k

Answer 15

h must be zero and k must be zero

Answer 16

how do you know its at the origin though

Answer 17

oh wait all the choices have the vertix set to (0,0) but if it isnt how do you know

Answer 18

\[ \Large x-h = \frac {1}{4p} (y-k)^2 \iff x = \frac {1}{4p} y^2 \]

Answer 19

the two equation left sides must match and the right side must match

Answer 20

ohhhhhh omg ok i get it

Answer 21

the two equations left sides must match and right sides

Answer 22

and thats how you know its at the origin?

Answer 23

yes. or by graphing it

Answer 24

ok then the directrix is 0-.25 which would = -1/4

Answer 25

but what about the focus?

Answer 26

correct. and the focus is (h+ p, k )

Answer 27

oh ok this is actually simplier than i thought! thank you so much!