Question

need help finding and graphing the focus and directrix of this equation

Answer 1

the equation is x = -(1/12)y^2. i have already graphed it on paper but need to find the focus and directrix.

Answer 2

What's the vertex?

Answer 3

i don't know how to find the vertex. that's my problem. after i find the vertex i know how to find the focus and directrix.

Answer 4

In the present form, the vertex is not too hard to find.

Usually, \(x = -\dfrac{1}{4}y^{2}\) is decoded as \(x - 0 = -\dfrac{1}{4}(y-0)^{2}\) ans we see quickly that the Vertex is (0,0), The Origin.

Answer 5

so what is p?

Answer 6

You need to find 4p from the rest of the information. In this case, -1/4.

Answer 7

so the focus is (-1/4, 0) and the directrix is 1/4 ?

Answer 8

No, that's 1/(4p), not p. You need just p.

Answer 9

so... 1/4(4) ? so 1?

Answer 10

Yes.

Answer 11

so the focus is (-1,0) and the directrix is 1?

Answer 12

Since we ignored the sign, though, it's still up to you to decide which side of the vertex the focus will be found. Does this one open up, down, left, or right?

Answer 13

it opens to the right so it's vertical so i'm pretty sure it's (-1, 0) and 1

Answer 14

I believe you have the focus and directrix correct, but it opens to the left or they are backwards. The focus has to be inside, right?

Answer 15

BTW "The directrix is 1" is not actually correct. The directrix is a line. It needs an equation of a line. The directrix is x = 1

Answer 16

i know that. i was just summarizing.

Answer 17

Take the time to communicate clearly EVERY TIME. It will pay dividends now and great dividends later.

Answer 18

@tkhunny can you help me with one more? \[y = \frac{ 1 }{ 4 }(x-2)^{2}\]

Answer 19

no tu el borrito es P y minues 22 el conornoto