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)   (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



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



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





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)   (Show Source): You can put this solution on YOUR website!
I have same comment for this parabola
if your parabola equation is then focus will be

so ->
Answer by Solver92311(821)   (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

From
I > Ø
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