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The 3D graphic below shows a pair of earrings based on elliptical shapes - Leaving Cert DCG - Question A-1 - 2014
Question A-1
The 3D graphic below shows a pair of earrings based on elliptical shapes. The drawing on the right shows the major and minor axes of an ellipse. A portion of the cu... show full transcript
Worked Solution & Example Answer:The 3D graphic below shows a pair of earrings based on elliptical shapes - Leaving Cert DCG - Question A-1 - 2014
Step 1
Locate the remaining points on the curve and draw the ellipse.
Answer
To locate the remaining points on the ellipse and draw it, follow these steps:
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Understand the Ellipse: An ellipse is defined by its semi-major axis (a) and semi-minor axis (b). Determine the lengths of these axes from the provided diagram.
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Determine the Center: Identify the center of the ellipse, which is where the major and minor axes intersect. This point is critical for the drawing.
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Locate Points: Using the formulas for an ellipse, which are:
rac{x^2}{a^2} + rac{y^2}{b^2} = 1
Compute points on the ellipse using the values of a and b. Calculate points for a range of angles (0°, 30°, 45°, etc.) to get a smooth curve.
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Draw the Ellipse: Connect the calculated points smoothly to complete the ellipse's shape.
Step 2
Locate the focal points of the ellipse.
Answer
The focal points (foci) of an ellipse can be found using the formula for the distance from the center to each focus:
Here, c is the distance from the center to a focus.
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Calculate c: Plug in the lengths of the semi-major axis (a) and semi-minor axis (b) into the formula.
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Identify the Foci: Place the foci at (±c, 0) along the major axis on the diagram.
By following these steps, the foci will be correctly located on the ellipse.