A solid sphere ‘S’ present in space (above X-Y plane) whose equation is (x – a) 2 + (y – b) 2 + (z – c) 2 = r 2
(i) A light source lies on the line 
= 
= 
above X-Y plane at infinite distance from X-Y plane. If a = c and
b = 0 then find the equation of the boundary of shadow of ‘S’ on X-Y plane.
(ii) A light source is at (5,0,3), a = c = 2, b = 0, r = 1. What is the locus name of boundary of shadow of ‘S’ on X-Y plane.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) x 2 + 2y 2 = 2r 2 (ii) Parabola
Sol. (i) The coming rays from the source form cylinder of infinite length. X-Y plane cuts this cylinder and form an ellipse in which major axis along x-axis of length 
r and minor axis along y-axis of length 2r.
⇒ equation of ellipse is x 2 + 2y 2 = 2r 2
(ii) Here coming rays form of a cone of infinite length. X-Y plane cuts the cone parallel to slant height hence figure formed is parabola.
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