Step 1 :
Let the origin be the vertex of the parabola and axis is along x - axis.
Since the parabola is open rightward
The equation of the parabola is $ y^2=4ax$
Step 2 :
Since the parabola passes through the point $A(10, 5)$, substituting the values for x and y we get,
$(10)^2=4 \times a \times 5$
$ \Rightarrow 100 = 20a$
$ \therefore a = 5$
Hence the focus of the reflector is 5, which is the midpoint of the diameter.