Question

this is for my virtual school class. I've gone through the lesson numerous times but im still struggling, any help?
Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1.

A.) f(x) = −one twenty-fourth (x − 1)2 − 5
B.) f(x) = one twenty-fourth (x − 1)2 − 5
C.) f(x) = −one twenty-fourth (x + 5)2 + 1
D.) f(x) = one twenty-fourth (x + 5)2 + 1

Answer 1

what is the vertical distance from the focus to the directrix?

Answer 2

btw none of these answer choices work, so there is a typo somewhere

Answer 3

i copy and pasted the answers but you never know i guess

Answer 4

well the issue is that the vertex is at (0,0) but none of the answer choices have a vertex of (0,0)

Answer 5

A and B have a vertex of (1,-5)

C and D have a vertex of (-5, 1)

Answer 6

whoops those were the wrong answers

Answer 7

sorry

Answer 8

a f(x) = −one fourth x2
b f(x) = one fourth x2
c f(x) = −4x2
d f(x) = 4x2
these are the right ones

Answer 9

ah, much better

Answer 10

are you able to find the vertical distance from the focus to the directrix?

Answer 11

i personally cant no

Answer 12

it might help to plot the two

Answer 13

here's a blank xy axis

Answer 14

there is the focus (0,1)

Answer 15

now I'm adding the directrix y = -1 shown as this horizontal dashed line