The vertex form equation of the parabola with vertex (h,k),
axis of symmetry: y = k, length of latus rectum = |4a|
is:
(y-k)² = 4a(x-h)
Substitute h=10, k=0, a=-1/4 since |4a|=1 and a < 0.
Edwin
Latus Rectum of 1 and the sign of a means that the focus is to the LEFT of the vertex. Both focus AND vertex are on the axis of symmetry, so x=0, and y=1/2 for the point (0, 1/2) as a endpoint for the latus rectum. Other endpoint is (0, -1/2 ).
Using either endpoint for the latus recturm, with the values substituted, and you can calculate and pick the correct value for "a".