Question

A parabola, with its vertex at the origin, has a directrix at y = 3. which statements about the parabola are true? select two options.

1. The correct options about parabola are:
The focus is located at (0,–3).
The parabola can be represented by the equation x^2 = –12y.
According to the statement
we have given that the vertex is at the origin and directrix at y = 3.
and from these given information and we have to find the all abot the parabola like its focus point etc.
So,
We know that the equation of parabola is
(x-h)^2 = 4p(y-k)
Here The vertex is (h,k). and the focus is at (h,k+p). and the directrix is   y(k – p.)
So, From the given information
Vertex at the origin means that h=0 and k=0
Directrix at y = 3 means that p=-3
Directrix at the y-axis means the parabola opens upwards.
Thus, the focus is: (0,-3)
And The p-value becomes
: 4(-3) = -12.
And from all these the equation of the parabola is becomes
(x)^2 = -12y
So, The correct options about parabola are:
The focus is located at (0,–3).
The parabola can be represented by the equation x^2 = –12y.