Courses
Courses for Kids
Free study material
Free LIVE classes
More

# 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.

Last updated date: 25th Mar 2023
Total views: 314.4k
Views today: 7.91k
Verified
314.4k+ views

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

${x^2} = 6y$