SOLUTION: State the focus of Parabola where the equation in y=-16x^2 a) 4 b) 16 c) -8 d) -4

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Question 1176570: State the focus of Parabola where the equation in y=-16x^2
a) 4
b) 16
c) -8
d) -4
Found 3 solutions by greenestamps, MathLover1, Solver92311:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


This is an example of a problem that is conceived extremely poorly.

The statement of the problem is sloppy: "...focus of Parabola..." "Parabola" with a capital p? and "focus of Parabola" instead of "focus of the parabola"?

And none of the answer choices makes sense; they are all single values, whereas the focus is an ordered pair of x and y values. Given the equation y=-16x^2, the vertex is at the origin, so we can assume the answer choices are supposed to be (0,4), (0,16), (0,-8), and (0,-4) instead of just 4, 16, -8, and -4.

Getting past the poor presentation of the problem, let's see what we find when we try to solve it.

The vertex form of the equation of a parabola is

y+=+%281%2F%284p%29%29%28x-h%29%5E2%2Bk

where the vertex is (h,k) and p is the directed distance from the directrix to the vertex, and from the vertex to the focus.

In this problem, the vertex is at (0,0), so the equation is

y=%281%2F%284p%29%29x%5E2

Since the coefficient of x^2 is -16, we have

1%2F%284p%29+=+-16
1+=+-64p
p+=+-1%2F64

With the vertex at (0,0 and p=-1/64, the focus is at (0,-1/64) -- not anywhere close to any of the answer choices.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
I have same comment for this parabola
if your parabola equation is y%5E2=-16x then focus will be
y%5E2+=+4px
so 4p=-16-> p=-4

Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


None of the answers given represent the focus of the given parabola. A focus of a parabola is a point. A parabola that is defined by an equation that contains two variables has a focus that is only correctly identified by an ordered pair. The given answers are simply numbers. Had you asked for the -coordinate of the focus, you still would be out of luck because that answer isn't on the list either.

For a vertex form equation of a parabola with a vertical axis of symmetry, such as the one that you were given is:



For this parabola, the vertex is at , the focus is at , and the equation of the directrix is .

You can do your own arithmetic to find the focus of your parabola.

John

My calculator said it, I believe it, that settles it

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