Question

A lamp has the shape of a parabola when viewed from the side. The lamp is centimeters wide and centimeters deep. How far is the light source from the bottom of the lamp if the light source is placed at the focus

Answer 1

The question is not complete so i have attached it.

Answer:

The light source is 2 cm from the bottom of the lamp

Explanation:

From the attached image, we can see that the parabola opens up with its vertex at the origin.

Now, the standard form of equation for a parabola is:

x² = 4ay

Looking at the parabola in the attachment, the top right edge of the lamp has a coordinate of (12,18)

Thus, we have;

12² = 4a(18)

144 = 72a

a = 144/72

a = 2

Looking at the parabola again, the line of symmetry is at x = 0

Thus, axis of symmetry is at x = 0.

Thus, focus is at (0, 2)

So, if the light source is placed at the focus, the distance of the light source from the bottom of the lamp is 2 cm