a spotlight throws a beam of light that is 25cm. in diameter. if the beam hits the stage floor at an angle of 60 degree with the horizontal, find an equation for the elliptical pool of light on the stage floor.
Answers
Given : a spotlight throws a beam of light that is 25cm. in diameter.
beam hits the stage floor at an angle of 60 degree with the horizontal,
To Find : an equation for the elliptical pool of light on the stage floor.
Solution:
Equation of Ellipse
x²/a² + y²/b² = 1
2b = 25 cm
=> b = 12.5
=> b² = 156.25
angle of 60 degree with the horizontal
sin 60° = 2b/2a
=> a sin 60° = b
=> a (√3 / 2) = b
=> a = 2b/√3
=> a = 25√3
=> a² = 625/3
=> a² = 208.33
equation for the elliptical pool of light on the stage floor.
= x²/208.33 + y²/ 156.25 = 1
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