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The graphic on the right shows an uplighter in the form of a hyperbolic paraboloid surface - Leaving Cert DCG - Question C-2 - 2013
Question C-2
The graphic on the right shows an uplighter in the form of a hyperbolic paraboloid surface. Fig. C-2 below shows the plan, elevation and end view of a similar uplig... show full transcript
Worked Solution & Example Answer:The graphic on the right shows an uplighter in the form of a hyperbolic paraboloid surface - Leaving Cert DCG - Question C-2 - 2013
Step 1
Draw the given plan of the uplighter.
Answer
To draw the plan of the uplighter, begin with the rectangular outline of the base. Ensure the dimensions are correct as per the given scale of 1:2. Next, sketch the parabolic contour ABC that has its vertex at B, projecting downwards along the defined axis. The three-dimensional aspect can be illustrated by emphasizing the curvature of the parabola.
Step 2
Project the given end view from the plan.
Answer
Using the drawn plan, project the end view by translating the parabolic shapes vertically. The curves should reflect the dimensions seen from the top view. Create the edges corresponding to the uplighter based on the elevations indicated, especially focusing on the transitions in height.
Step 3
Step 4
Determine the asymptotes to the double hyperbola in elevation.
Answer
Identify the center point of the double hyperbola, which serves as the intersection of the asymptotes. Use the coordinates of the vertices V1 and V2 to establish lines extending from the center point, which represent the asymptotes of the double hyperbola. Ensure accurate representations of these lines, as they will help in understanding the behavior of the curves.