Question

Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8

Answer 1

multiple choice?

Answer 2

yeah

Answer 3

@gnorris

Answer 4

f(x) = −one eighth (x − 2)^2 + 6
f(x) = one eighth (x + 2)^2 + 8
f(x) = one eighth (x − 2)^2 + 6
f(x) = −one eighth (x + 2^)2 + 8

Answer 5

alright let me see if i can

Answer 6

f(x) = -1/8 (x - 2)2 + 6
f(x) = 1/8 (x - 2)2 + 6
f(x) = -1/8 (x + 2)2 + 8
f(x) = 1/8 (x + 2)2 + 8

Answer 7

i wrote it out better

Answer 8

yeah

Answer 9

urghh i cant be much help all i can say is its not the third choice

Answer 10

really that is the one i thought it was

Answer 11

The \[\frac{ 1 }{ 4p }\] is the most confusing part for me

Answer 12

no it isn't the third choice
Go through the steps. Focus is at (2,4), directrix is at y = 8. Distance between focus and directrix is |8-4| = 4. Vertex (h,k) is at spot halfway between focus and directrix, or
(h,k)=(2,8+4/2)=(2,6)
Fill in the blanks:
y=a(x−h)2+k
y=a(x−2)2+6

To find the value of a, use
a=1/4p
where p is the distance from the focus (2,4) to the vertex (2,6). draw a sketch; the parabola wraps around the focus and veers away from the directrix (and does not cross it!) If the parabola opens upward, like a bowl, a will be greater than 0. If the parabola opens downward, like an inverted bowl, a will be less than 0.

Answer 13

uhh ok that makes a little more sense

Answer 14

could you use the distance formula

Answer 15

to find p i mean