SOLUTION: 2. Choose the equation of the parabola with a vertex at the origin and a focus at (0, –3). 1. y=-1/3x 2. y=1/12x^2 3. y=-1/3x^2 4. y=1/12x^2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 2. Choose the equation of the parabola with a vertex at the origin and a focus at (0, –3). 1. y=-1/3x 2. y=1/12x^2 3. y=-1/3x^2 4. y=1/12x^2       Log On


   

Question 189988: 2. Choose the equation of the parabola with a vertex at the origin and a focus at (0, –3).
1. y=-1/3x
2. y=1/12x^2
3. y=-1/3x^2
4. y=1/12x^2
Answer by cutepiscean5(19) About Me  (Show Source):
You can put this solution on YOUR website!

we have the vertex as (0,0) and focus as (0,-3) , since the x-coordinate of both the vertex and focus are the same, it means the parabola is a vertical parabola.
The form of a vertical parabola is given by:
+4p%28y-k%29+=+%28x-h%29%5E2+
where (h,k) is the vertex (here it is (0,0))
p = distance between the vertex and the focus of the parabola.
we are given the coordinates of focus as (0,-3), thus the y-coordinate here is equivalent to k + p
=> +-3+=+0+%2B+p+
=> +p+=+-3+
we plug in all the values into the equation and get:
+4%2A%28-3%29%28y-0%29+=+%28x-0%29%5E2+
simplifying further we get:
+-12%2Ay+=+x%5E2+
=> +y+=+-1%2F12%2Ax%5E2+
so out of choices 2 and 4 which ever corresponds to our answer is the correct one. (there is a misprint in the choices that has been given for 2 and 4)
Hope this helps you.