In need of help please. Find an equation for the parabola that has it's vertex at the origin and focus F (6,0)
2006-11-28 07:22:23 · 7 answers · asked by cam1560 3 in Education & Reference ➔ Homework Help
this is an example becuase im not doing it for you.
Things you need to know
Formula for a parabola (with vertical symmetry): (x-h)^2 = 4a(y-k) where "h" and "k" are the x and y corrdinates of the vertex, and "a" is the distance from the vertex to the focus.
Coordinates of the vertex: (h,k) - these tell you how far to shift your parabola from the origin.
Coordinates of the focus: (h, k+a) - if a is the distance from vertex to focus, then k+a should give you the point of the focus
Formula of the directrix: y = k-a -- the vertex lies halfway between the focus and directrix, so subtracting the distance from the vertex to the focus will give you the directrix.
Please ask your teacher if you do not understand the reasoning behind any of these formulas.
~~~~~~~~~~~~~~~~~~~~~
Now, from what you are given, a vertex at (0,0) and a focus at (0,4) you can see that since the y coordinate is the one that changes, the focus lies above the vertex (not left or right) so it must be a vertically symmetrical parabola. You can also tell that it opens upward, since the focus lies inside the parabola and it is above the vertex. This means that the directrix is a flat line below the parabola.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
On to solving your problem:
Vertex (h,k) = (0,0)
Focus (h,k+a) = (0,4) so k+a = 4 -- from the vertex you know that k=0, so 0+a = 4, or a = 4
Remember the formula for the directrix was y = k-a. Plug in what you know and you get y = 0-4, or y = -4
hope it help.... where's my 10 points?¿?
2006-11-28 07:34:32 · answer #1 · answered by tinkerbell03 2 · 1⤊ 1⤋
I consistently attempt to respond to truly and as though I have been incredibly chatting with the guy....I additionally choose to place a splash humor into my answer if plausible. I never say something rude till the guy incredibly ticks me off with their question and that i've got faith they deserve a reliable "puter-spank" i've got quite gotten ultimate solutions with those... LOL
2016-12-14 08:16:08 · answer #2 · answered by Anonymous · 0⤊ 0⤋
you said "answer to receive 10 points!?" ok, I'm ready for my 10 points!!
2006-11-28 07:25:01 · answer #3 · answered by lily 5 · 0⤊ 1⤋
Do your own home work. How do you expect to learn anything.
2006-11-28 07:30:32 · answer #4 · answered by Blue Eyes 4 · 1⤊ 1⤋
do ur home work by urself
2006-11-28 07:32:39 · answer #5 · answered by LOST 6 · 1⤊ 1⤋
Two will do. Thanks!
2006-11-28 07:32:35 · answer #6 · answered by shabuandshabu 2 · 1⤊ 1⤋
I'll just take two, thanks.
2006-11-28 07:25:46 · answer #7 · answered by Anonymous · 1⤊ 1⤋