Question 1135977
<br>
For me, the most useful form of the equation of a parabola (that opens right or left) is<br>
{{{x-h = (1/(4p))(y-k)^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>
{{{x-0 = (1/(1/10))(y-0)^2}}}<br>
So...
(1) the vertex is (0,0);
(2) 4p=1/10 so p=1/40, so the focus is (1/40,0) and the directrix is x = -1/40; and
(3) the focal width is 4p = 1/10 = 0.1<br>
The first answer choice is the correct one.