Answer:
(c) x = -1/11(y -3)²
Explanation:
You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).
Equation
The directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.
The vertex form of the equation is ...
x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)
Application
Here, we have ...
p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix
and
(h, k) = (0, 3)
so the equation is ...
x = 1/(4(-11/4))(y -3)² +0
x = -1/11(y -3)²