Question

What are the vertex, focus, and directrix of the parabola with equation x=-3y^2?

Please show all steps! Will give medal and fan for best answer!

Answer 1

Do I plug -3y^2 into that..?

Answer 2

uhm.. no

Answer 3

what is (h,k) is this case?

Answer 4

(x,y).. vertex.. I dont know. I'm confused with this. Sorry.

Answer 5

http://www.purplemath.com/modules/parabola.htm

Answer 6

x=-3y^2 <==> y^2 = (-1/3)x yes?

Answer 7

@surjithayer

Answer 8

so what is the vertex in this case?

Answer 9

0,0?

Answer 10

correction: standard form should have been
(y + k)^2 = 4 (p) (x - h)

Answer 11

so how do we get 4 to show up in the equation (y - 0)^2 = (-1/3) (x - 0)?

Answer 12

Put it in place of y?

Answer 13

no, we can multiply the right side by (4/4) and that won't change the equation

(y - 0)^2 = (4/4) (-1/3) (x - 0)
(y - 0)^2 = (4) (1/4) (-1/3) (x - 0)
(y - 0)^2 = (4) (-1/12) ((x - 0)

so now what is the p?

Answer 14

so the p is 4 then, right?

Answer 15

or -1/12?

Answer 16

yes p is -1/12. So what is the distance from the vertex to the focus?

Answer 17

12?

Answer 18

no, it's 1/12

Answer 19

That's what I meant lol.

Answer 20

ok, so which way does the parabola opens?

Answer 21

To the right..

Answer 22

is p the directrix?

Answer 23

no it opens to the left

Answer 24

and no p is not the directrix, although we can use it to determine the directrix

Answer 25

What does p stand for then? focus?

Answer 26

p stands for the distance from the vertex to the focus

Answer 27

which we found out to be 1/12