SOLUTION: Can someone tell me what I'm supposed to do? I don't get it. I'm supposed to find the focus and directrix. {{{y=x^2/16}}} {{{y-5=(1/4)(x+3)^2}}} I have all of these formulas bu

Question 913811: Can someone tell me what I'm supposed to do? I don't get it. I'm supposed to find the focus and directrix.

I have all of these formulas but I have no clue where to put what. It's starting to irritate me. A lot.
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
This is not a solution, but just advice:

Study how the equation of a parabola is derived using the distance formula, the meaning and use of focus and directrix, and the definition of a parabola. Simplify the distance formula equation and check how the resulting formula appears. That would be how to derive the equation of a parabola.

What you want to do is work in the other direction, so you would use the parts the resulting derived parabola equation to find the focus and directrix.

Like I say, this is advice or guidance, but not the answer you requested.
Your textbook should show a very good derivation for the equation of a parabola. Say if otherwise.

Note that in your second equation, the vertex would have moved from the standard reference (0,0) to the new vertex point (-3,5).
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the focus and directrix.

***
Basic form of equation for a parabola that applies here:
(x-h)^2=4p(y-k), (h,k)=coordinates of the vertex, p=distance from vertex to focus and to directrix on the axis of symmetry
..

x^2=16y
This is a parabola that opens up with vertex at the origin
axis of symmetry: x=0 or y-axis
4p=16
p=4
focus:(0,4)
directrix: y=-4
..

(x+3)^2=4(y-5)
This is a parabola that opens up with vertex at (-3,5)
axis of symmetry: x=-3
4p=4
p=1
focus:(-3,6)
directrix: y=4
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