Question

Find an equation of the parabola with directrix y=6 and focus (0,2).

Answer 1

vertex is halfway between d and f

Answer 2

so directrix would be same length between vertex right?

Answer 3

yeah; -4ay = x^2 is what we wanna transform; and a = half the distance between d and f

6-2 = 4/2 = 2.. a =2

Answer 4

??? lol i'm lost.

Answer 5

-4(2)(y-4) = x^2 accounts for the vertex i think

Answer 6

the vertex is at (0,4) whic is half way between the directix and the focus

Answer 7

the distance from the focus to the vertex is defined in most cases as 'a'

-4(2)(y-4) = x^2

y-4 = (-1/8)x^2

y = (-1/8)x^2 +4

Answer 8

ok i get everything else, just why did u multiply -4(2)?

Answer 9

the focus is important; and it has to be placed in the right spot in order for the parabola to be defined appropriately; the distance between focus and vertex EQUALS the distance between vertex and directix; on here that distance = 2

Answer 10

it is the geometric definition for a parabola

Answer 11

4ay = x^2 is the generic version of it

Answer 12

since the focus is under the vertex, it opens down; so I need a -4ay to = x^2

Answer 13

since the vertex is not at the origin; we make note of it in the equation;

-4a(y-4) = x^2

Answer 14

we didn't learn that formula, i'm trying to get the answer off of the equation y=a(x-h)^2+k

Answer 15

there are many parabolas with a vertex as 0,4

Answer 16

without any other points to compart with, you have to use the the geometric definition

Answer 17

all points along the curve are equidistance from a perpendicular line from the directix and the focus.

Answer 18

ohhhh i see that, so vertex =0,4. and so distance is 2. so u got y-4=(-1/8)x?

Answer 19

well; x^2 but yeah

Answer 20

ok i kind of see that.