Question

Derive the equation of the parabola with a focus at (4, −7) and a directrix of y = −15. Put the equation in standard form.

f(x) = one sixteenthx2 − 8x + 11

f(x) = one sixteenthx2 − 8x − 10

f(x) = one sixteenthx2 − one halfx + 11

f(x) = one sixteenthx2 − one halfx − 10

Answer 1

f(x)=(1/16)^2 is it written like this?

Answer 2

Yes, but whats the other half of the equation?

Answer 3

Not sure yet I was just making sure that's how it was written numerically. Do you know what the focus is? I don't want to just give you the answer, but I'll teach you

Answer 4

Thanks :) and the focus is (4, -7)

Answer 5

No I mean do you know the.. hmm definition of the focus? because that is important

Answer 6

Oh. No, I have this class on flvs and it literally is so difficult to understand, I'm guessing that's the point of the parabola though, like where it starts.

Answer 7

No, the focus of the parabola is a point inside of it. I'll draw you a diagram. (I took alg. 2 in school, redid it on FLVS and like.. ugh. it sucked. I feel your pain.)

Answer 8

Thanks :) and I know! It's ridiculous.

Answer 9

sorry for that random line

Answer 10

But the equation for the focus of a vertical parabola is
4p(y-k)=(x-h)^2

Answer 11

you know what the variables stand for?

Answer 12

It's ok lol. and ok :) that makes sense and no.

Answer 13

ok h is the horizontal distance. This might be difficlt without a diagram, let me go find my math book. 10 minutes tops

Answer 14

Ok tysm

Answer 15

OMG LIKE WHAT IS LIFE I REMEMBER NOW THIS BOOK I LOVE IT

Answer 16

sorry okay the directrix is equal y=-p

Answer 17

here I will copy what the book says

Answer 18

"You know that the graph of y=ax^2 is a parabola that opens up or down with vertex (0,0) and axis of symmetry is x=0. On any parabola, each point is equidistant from a point called the FOCUS on the line called the DIRECTRIX."

does that make sense so far?

Answer 19

Yes :)

Answer 20

ok the focus lies on the axis of symmetry.

the directrix is perpendicular to the axis of symmetry

the vertex lies halfway between the focus and directrix.

Answer 21

Alrighty

Answer 22

does that make sense?

Answer 23

Yeah :)

Answer 24

Alright. The equation the parabola opens up or down ns has vertex of (0,0) can also be written as x^2=4py. (this is where p becomes important). Parabolas also open left and right , where y^2=4px

Answer 25

the focus and the directrix lie |p| units from the vertex.