Write an equation in standard form for the parabola with focus (-4,0) and directrix x=4

Answer 1

Since the directrix is the vertical line x=4, the axis of the parabola is the horizontal line containing the focus.

So, the axis is the horizontal line y = 0 (the x-axis).

The vertex is on the axis and lies halfway between the focus and directrix. So, the vertex is (0,0)

Equation of parabola: (y-0)² = 4p(x-0).

p is the directed distance between the vertex and focus (since the focus is to the left of the vertex, p < 0.

So, p = -4. Note: had the focus been to the right of the vertex, then p would have been positive.

Equation of parabola: (y-0)² = -16(x-0). Simplify to get y² = -16x.