How Do You Calculate the Depth of a Parabolic Reflector?

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SUMMARY

The discussion focuses on calculating the depth of a parabolic reflector, specifically a TV dish with a diameter of 10 cm and a focus located 2 cm from the vertex. The equation for a parabola with a vertical axis of symmetry is utilized, passing through the origin with the focus at (0, 2). By substituting x = 5 into the parabola's equation, participants aim to determine the corresponding y-value, which represents the depth of the reflector.

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  • Understanding of parabolic equations and their properties
  • Familiarity with the geometric definition of a parabola
  • Basic algebra skills for solving equations
  • Knowledge of coordinate systems and graphing
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  • Study the standard form of a parabolic equation: y = ax^2
  • Learn how to derive the vertex and focus of a parabola
  • Explore applications of parabolic reflectors in optics and telecommunications
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Students in mathematics, engineers working with reflective surfaces, and anyone interested in the practical applications of parabolic shapes in technology.

dillonwerd
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This is my first post here so I hope I put it in the proper place.

Here's the basic info on the question.

parabolic reflector (like a tv dish) has diameter of 10cm, focus is 2 cm from the vertex. Find the depth.

Thanks in advance for an help. I've been stuck on this for a while! Getting frustrated.
 
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First write down the equation for a parabola with y-axis a axis of symmetry, passing through (0,0), focus at (0, 2). Now, when x= 5, what is y?
 

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