Question

A flashlight with a parabolic reflector has the light bulb placed at the focus. The distance from the light bulb to the side of the flashlight, called the focal diameter, is 3cm. Determine the equation for the Parabola.

Answer 1

From the figure, Focal diameter is 6cm.

Focal diameter is nothing but a perpendicular from focus on the parabola (i.e, latus rectum)

$\Rightarrow$ Latus rectum = 6cm --- (Eq 1)

The given parabola is vertically and opening upward with vertex (0,0)

So, the standard equation of the parabola is

$\Rightarrow {x^2} = 4ay$

Focus (0,a)

Latus Rectum = 4a -- (Eq 2)

From equation 1 and 2

$\Rightarrow 4a = 6$

So, the equation of parabola is

${x^2} = 6y$

So, this is your required answer

NOTE: - In this type of question first check out the direction of opening of parabola after that write the standard equation and compare from given conditions, then you’ll get your answer.