MathDB

A unit sphere is centered at

(0, 0, 1)

. There is a point light source located at

(1, 0, 4)

that sends out light uniformly in every direction but is blocked by the sphere. What is the area of the sphere’s shadow on the

x-y

plane? (A point

(a, b, c)

denotes the point in three dimensions with

x

-coordinate

a

y

-coordinate

b

, and

z

-coordinate

c

)

Problem Statement