Hello, jeunesse27!
Who wrote this problem?
The term "diameter" is usually reserved for circles.
A lamp with a parabolic reflector is shown in the figure. . Right!
The bulb is placed at the focus and the focal diameter is 20 cm. . latus rectum?
Find the width $\displaystyle CD$ of the opening 15 cm from the vertex, to the nearest cm.
. . $\displaystyle (a)\;35 \qquad (b)\;38 \qquad (c)\;40 \qquad (d)\;39\qquad (e)\;37$ I'll take a guess at what's going on . . . Code:

15
C o     +     o D

F
(10,p)o    o    o (10,p)

* p *
*  *
*  *
    *o*         
V
The equation is: .$\displaystyle x^2 \:=\:4py$
. . where $\displaystyle p$ is the distance from the vertex $\displaystyle V$ to the focus $\displaystyle F.$
The length of the latus rectum is $\displaystyle 4p.$
. . Hence: .$\displaystyle p \,=\,5$
The equation is: .$\displaystyle x^2 \:=\:20y$
If $\displaystyle y = 15$, we have: .$\displaystyle x^2 \:=\:20(15) \:=\:300 \quad\Rightarrow\quad x \:=\:\pm\sqrt{300}\:=\:\pm10\sqrt{3}$
Therefore: .$\displaystyle CD \;=\;2(10\sqrt{3}) \;=\;34.64191615 \;\approx\;35\text{ cm}\;\;\;\text{ answer }(a)$