Given: Parabolic reflector is 5 cm deep & its diameter is 20 cm
Need to find: Distance of its focus from the vertex.
Reflector is 5 cm deep, i.e., OD = 5 cm
Diameter of the mirror is 20 com, i.e., BC = 20 cm
Let, the equation of the parabola is y2 = 4ax, where a is the distance of the focus from the vertex.
The x-coordinate of the points B and C is 5.
D is the middle point of BC which is upon the x-axis.
So, we can say that BD = CD = 10 cm.
So, the coordinate of the point B is (5, 10)
Putting the values of the equation,
y2 = 4ax
⇒ 100 = 4a x 5
⇒ 20a = 100
⇒ a = 5
That means, the focus is 5 cm far from the vertex.
