Question

Help me please…………………………

Answer 1

Answer:

Correct option: First one -> $x^2 = -12y$

Step-by-step explanation:

The focus and the vertex have the same x-coordinate, so we have a vertical parabola. The standard equation for this parabola is:

$y = a(x-h)^2 + k$

If the vertex is at the origin, we have that:

$(h, k) = (0,0)\\h = 0, k = 0$

If the focus is at (0,-3), we have that:

$(h, k+p) = (0, -3)$

$p = 1/4a$

$k + p = -3$

$1/4a = -3$

$a = -1/12$

So we equation of the parabola is:

$y = -x^2/12$

$x^2 = -12y$

Correct option: First one