Question

1. Find the equation of a parabola with a focus of (0, -6) and directrix y = 6.

Max points

Answer 1

9514 1404 393

Answer:

1. (d) y = -1/24x²
2. (b) y = 1/36x²

Explanation:

1. The point halfway between the focus and directrix is the origin. That is, the vertex of the parabola is the origin. Then its equation can be written ...

y = 1/(4p)x²

where p is the distance from the vertex (origin) to the focus. Here, that distance is -6, so 4p = -24 and the parabola's equation is ...

y = -1/24x²

__

2. Same deal. The vertex is the origin, but this time the focus is above the origin by 9 units. Then the equation is ...

y = 1/36x²