SOLUTION: Please help me find the focus and the dirctrix of the parabola 16x^2=y. There are 4 choices for an answer: 1. Focus (0,4), directrix y=-4 2. Focus (0,1/4), directrix y=-1/4 3.

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Question 150361: Please help me find the focus and the dirctrix of the parabola 16x^2=y.
There are 4 choices for an answer:
1. Focus (0,4), directrix y=-4
2. Focus (0,1/4), directrix y=-1/4
3. Focus (0,1/16), directrix y=-1/16
4. Focus (0,1/64), directrix y=-1/64
Thank you for your time and help, Natalie!
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
16x^2=y.
There are 4 choices for an answer:
1. Focus (0,4), directrix y=-4
2. Focus (0,1/4), directrix y=-1/4
3. Focus (0,1/16), directrix y=-1/16
4. Focus (0,1/64), directrix y=-1/64
Thank you for your time and help, Natalie!
----------------
The standard from for parabolas is x^2=4py
So y = x^2/4p = 16x^2
x^2/4p = 16x^2
4p = x^2/16x^2 = 1/16
p = 1/64
P is the distance from the Origin to the directrix, and (0,p) is the focus.
That's answer #4.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 0, 0. Here's your graph:
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