Finding the Radius of a Paraboloid Spotlight

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To find the radius of a paraboloid spotlight, either equation X^2 = 4ay or y^2 = 4ax can be used, depending on the orientation of the parabola. The spotlight is 5 inches deep with its focus 2 inches from the vertex. The choice of equation affects the axis along which the spotlight points; the first points along the y-axis while the second points along the x-axis. Both equations represent the same relationship, differing only in variable naming. The radius of the opening of the spotlight can be calculated using these parameters.
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Hi

In this queation which equation we use X^2 = 4ay or y^2 = 4ax and why ?

A paraboloid is formed by revolving a parabola about its axis . A spotlight in the form of a parabolid 5 inches deep has it's foucs 2 inches from the vertex . Find to one decimal place , the raduis R of the opening of the spotlight ...
 
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Both equations represent the same relation. The names of variables have just been flipped. In the first equation the spotlight would be pointing along the y-axis. In the second equation it would be pointing along the x-axis.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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