Find the vertex, focus, and directrix of the parabola.
xequals StartFraction 1 Over 28 EndFraction
y squared
To find the vertex, focus, and directrix of the parabola given by the equation x = 1/28y^2, we first need to rewrite the equation in standard form.
The standard form of the equation of a parabola with the vertex at the origin is given by x = 4py, where (0,p) is the focus of the parabola and y = -p is the directrix.
In this case, we have x = (1/28)y^2, which can be rewritten as x = (1/28)(4p)y.
Comparing this with the standard form, we get p = 1/112. This means that the vertex of the parabola is at (0,0) and the focus is at (0,1/112). The directrix is the horizontal line y = -1/112.
Therefore, the vertex of the parabola is (0,0), the focus is (0,1/112), and the directrix is the horizontal line y = -1/112.