SOLUTION: Find the equation of the parabola described: Focus at (0,2); vertex at (0,0). Graph the parabola and the directrix. Please explain. Thanks

Question 114527: Find the equation of the parabola described: Focus at (0,2); vertex at (0,0). Graph the parabola and the directrix. Please explain. Thanks
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The first thing we know about this parabola is that the axis of symmetry is the line x = 0. We know this because the both the focus and the vertex have to lie on the same line and the only line that passes through both (0,2) and (0,0) is x = 0, or the y-axis.

The next thing is to determine the distance between the focus and the vertex. We can really just tell by inspection that the distance is 2 because both points are on a vertical line with the y coordinates differing by 2. But, just to show the general case, lets use the distance formula:

Now the equation for a parabola is where p is the distance from the focus to the vertex, and the vertex is at point(h,k). So,

The directrix is a line perpendicular to the axis of symmetry -p units distant from the vertex. Since our parabola has a vertical line as an axis of symmetry, the directrix must be a horizontal line. The only horizontal line that is -2 units from the vertex (0,0) is y = -2.

The green line is the directrix

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