Determine the radius of the opening of the spotlight
in Algebra 2 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The paraboloid has two cross-sections: circle and parabola, illustrated below in 2D and 3D. In the 3D projection (which can be viewed using 3D glasses—left eye red filter, right eye—green/blue filter) a horizontal plane intersects the paraboloid 9in from the vertex. In the 2D vertical section, the parabola with its focus can be seen and the blue line intersects the parabola. The blue line is the plane in the 3D projection as seen on edge. The equation of the 2D picture is y=x²/4f=x²/12 where f is the focus at 3in when (0,0) is the vertex.

The radius of the searchlight can be calculated by putting y=9:

9=x²/12, x²=108=r² where r is the required radius. r=√108=6√3=10.39in. approx.

Equation of paraboloid: z=(x²+y²)/12.

by Top Rated User (695k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
84,102 questions
89,036 answers
1,992 comments
6,726 users