Parabola - 1

1. Find the focus, directrix, and vertex for the parabola x² = -16y

For x² = 4ay

Focus is (0,a), directrix is y = -a, and vertex is (0,0)

Write the given equation as x² = 4 (-4)y

Hence focus is (0,-4), directrix is y = 4, and vertex is (0,0).
The parabola opens downward.

2. Find the equation of the parabola that satisfied the following conditions.

Vertex (0,0), latus rectum = 16, opens to the right.

Latus rectum for standard parabola = |4a|
Hence |a| for the given parabola = 4
As vertex is at (0,0) and the parabola open to the right focus is (4,0)
The standard equation is y² = 4ax.

The equation of the given parabola = y² = 4*4x = 16x