Question 1135976
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For me, the most useful form of the equation of a parabola (that opens up or down) is<br>
{{{y-k = (1/(4p))(x-h)^2}}}<br>
In this form...
(1) the vertex is (h,k);
(2) p is the (directed) distance from the vertex to the focus; which means -p is the directed distance from the vertex to the directrix; and
(3) 4p is the focal width (length of the latus rectum)<br>
Written in that form, the equation in your example is<br>
{{{y-0 = (1/20)(x-0)^2}}}<br>
So...
(1) the vertex is (0,0);
(2) 4p=20 so p=5, so the focus is (0,5) and the directrix is y = -5; and
(3) the focal width is 4p = 20<br>
The first answer choice is the correct one.