Question

A parabola, with its vertex at (0,0), has a focus on the negative part of the y-axis. Which statements about the parabola are true?

Check all that apply.

The directrix will cross through the positive part of the y-axis.

The equation of the parabola will be in the form y2 = 4px where the value of p is negative.

The equation of the parabola will be in the form x2 = 4py where the value of p is positive.

The equation of the parabola could be y2 = 4x.

The equation of the parabola could be x2 = y.

Answer 1

option 1 and 5

Explanation:

Answer 2

In the attached diagram you can see all four possible placement of a parabola with vertex at origin.

You know that parabola has a focus on the negative part of the y-axis. Then you chould consider the 4th placement of parabola.

As you can see the directrix crosses through the positive part of the y-axis. (Option A is true).

The equation of parabola is
`y=-4ax^2`, where a is a positive number, then all four remaining options are false, because each of these options gives you wrong equation of parabola.

Answer: correct choice is A.