Question

Which is the equation of a parabola with vertex (0,0) and directrix y= 4

a. Y^2 = -8x
b. Y^2 = -16x
c. X^2 = -8y
d X^2 = -16y

Answer 1

D.
`x^(2) = -16\cdot y`

Explanation:

The vertex form of the equation of the parabola centered in the origin, with axis of symmetry in the x-axis and directrix in the first and second quadrants is described by the following formula:

`4\cdot p \cdot y = x^(2)`,
`p < 0` (1)

Where:

`y` - Dependent variable.

`x` - Independent variable.

`p` - Focus distance.

If we know that vertex is located at (0, 0) and the directrix pass through (4, 0), then the focus distance (distance of the vertex with respect to that point) is -4, and the equation of the parabola is
`x^(2) = -16\cdot y`.

Hence, the right choice is D.