Question

http://prntscr.com/d8fhh5

Answer 1

you know that
x = a(y-k)² + h
for a sideways parabola

To find the axis of symmetry start with the vertex. The vertex of this parabola is (5,-1)
and the axis of symmetry is at the y ordinate
so a standard set of coordinates is (x,y), in your case, (5,-1), hence x=5, y=-1
so our axis of symmetry is at y=-1

so y+1=0, if we rearrange it
so we can substitute this into
x = a(y-k)² + h

to get

x=a(y+1)² + h

h is the x ordinate so h=5
so we get

x=a(y+1)² +5


The focus is (h+1/(4a), k).
The directrix is (h-1/(4a), k).

idk how to find the value of a

Answer 2

just for reference
the vertex is at the point (h, k)
at the centre of the curve