Question 189988


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(y-k) = (x-h)^2 }}}

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 + p }}}
=> {{{ p = -3 }}}

we plug in all the values into the equation and get:

{{{ 4*(-3)(y-0) = (x-0)^2 }}}

simplifying further we get:

{{{ -12*y = x^2 }}}
=> {{{ y = -1/12*x^2 }}}

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.