- anonymous

Find the vertex, focus, directrix, and focal width of the parabola.
x = 4y^2

- schrodinger

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- perl

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

- anonymous

ok what do i do wuth that formula

- perl

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

oh so p = 1/16?

- perl

yes

- perl

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

- perl

it is centered at the origin

- anonymous

how do we find h and k

- anonymous

ok the focal width is .25

- perl

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

- perl

yes that is correct

- anonymous

is the focal width represented as a single letter?

- perl

4 times that value of p

- anonymous

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

- perl

h must be zero and k must be zero

- anonymous

how do you know its at the origin though

- anonymous

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

- perl

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

- perl

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

- anonymous

ohhhhhh omg ok i get it

- perl

the two equations left sides must match and right sides

- anonymous

and thats how you know its at the origin?

- perl

yes. or by graphing it

- anonymous

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

- anonymous

but what about the focus?

- perl

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

- anonymous

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.