Question

Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7

Answer 1

\[
x = 4py^2
\]

Answer 2

Where \(p\) is the the \(y\) of the focus minus the \(y\) of the vertex.

Answer 3

The vertex is halfway between focus and directrix.

Answer 4

mhm

Answer 5

so is it a sideways parabola?

Answer 6

Yeah it looks like it.

Answer 7

so p=3 but how do i know if the focus is (3,0) or (0,3)?

Answer 8

no, \(p=7\)

Answer 9

wrong problem lol. i waslooking at another one

Answer 10

so this parabola has the vertex at (0,0) and then what do i do from then on?

Answer 11

All you ever have to do is find \(p\).

Answer 12

and figure out if it is horizontal or vertical

Answer 13

You can use:\[\Large
p = \frac{x_{focus}-x_{directrix}}{2}
\]
or\[\Large
p = x_{focus}-x_{vertex}
\]

Answer 14

When your directrix is \(x =b\), then you have \(x=4py^2\)

When your directrix is \(y=b\) then you have \(y=4px^2\).

Answer 15

You can can translate it by \((x_0,y_0)\), using \((x,y)\to (x-x_0,y-y_0)\)

Answer 16

@wio i got x=28y^2 but that's not one of the answer choices

Answer 17

what are the answer choices

Answer 18

y = one divided by twenty eightx2

x = one divided by twenty eighty2

-28y = x2

y2 = 14x

Answer 19

y=(1/28)x2
x=(1/28)y2

are the first and second choirces my bad

Answer 20

the 2 is squared

Answer 21

My bad it was \(4px = y^2\)

Answer 22

So you should get \(1/28\)

Answer 23

\When your directrix is \(x =b\), then you have \(4px=y^2\)

When your directrix is \(y=b\) then you have \(4py=x^2\).

Answer 24

oh okay, THENK YOU SO MUCH