Let LAM be the parabolic reflector such that LM is its diameter and $\mathrm{AN}$ is its depth. It is given that $\mathrm{AN}=5 \mathrm{~cm}$ and $\mathrm{LM}=20 \mathrm{~cm}$
$$
\therefore \quad \mathrm{LN}=10 \mathrm{~cm}
$$
Taking $\mathrm{A}$ as the origin, $\mathrm{AX}$ along $\mathrm{x}$-axis and a line through A perpendicular to $\mathrm{AX}$ as $\mathrm{y}$-axis, let the equation of the reflector be
$$
y^2=4 a x
$$
The point $\mathrm{L}$ has coordinates $(5,10)$ and lies on (i).
Therefore,
$$
10^2=4 a \times 5 \Rightarrow a=5
$$
So, the equation of the reflector is
$$
y^2=20 x
$$


$$
\text { Its focus is at }(5,0) \text { i.e. at point } N \text {. }
$$






$$
\text { Hence, the focus is at the mid-point of the given diameter. }
$$