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The graphic below shows the Irish Credit Union logo - Leaving Cert DCG - Question A-1 - 2016
Question A-1
The graphic below shows the Irish Credit Union logo. It consists of two ellipses which share the same minor axis. The drawing on the right shows the completed inner ... show full transcript
Worked Solution & Example Answer:The graphic below shows the Irish Credit Union logo - Leaving Cert DCG - Question A-1 - 2016
Step 1
Locate additional points on the curve and draw the second ellipse.
Answer
To locate additional points on the curve of the second ellipse, follow these steps:
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Determine the Major and Minor Axes:
The major axis is the longest diameter of the ellipse, while the minor axis is the shortest. Use the given dimensions from the inner ellipse to find these axes. -
Equation of the Ellipse:
If the semi-major axis is 'a' and the semi-minor axis is 'b', the standard equation is given by:Substitute the values of the semi-major and semi-minor axes for the outer ellipse.
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Calculate Additional Points:
Compute several values of 'x' to determine corresponding 'y' values using the above equation. Calculate points in the first quadrant and then reflect them in other quadrants. -
Plot the Points:
Draw the additional points on the graph to form the shape of the second ellipse. -
Curve Completion:
Connect all the points smoothly to complete the outer ellipse.
Step 2
Locate the focal points of the second ellipse.
Answer
To locate the focal points of the second ellipse, follow these steps:
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Identify the Semi-Major and Semi-Minor Axes:
Confirm the lengths 'a' and 'b' for the second ellipse. -
Calculate the Distance to Foci:
The focal points (F) can be found using the formula:where 'c' is the distance from the center of the ellipse to each focus.
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Determine the Locations of the Foci:
The foci will be located along the major axis at (±c, 0) if the major axis is horizontal, or at (0, ±c) if it's vertical. Plot these points on the figure.