The 3D graphic below shows the proposed design for the new children’s hospital in Dublin. It consists of an ellipse and two inner circular arcs. The drawing on the right shows the major and minor circles for the ellipse. Portions of the ellipse and the inner arcs are also shown. (a) Locate the remaining points on the ellipse and draw the curve. (b) Locate the focal points of the ellipse. (c) Locate the centre point for the lower arc and complete the drawing.

Leaving Cert DCG Conic Sections: The 3D graphic below shows the p

The 3D graphic below shows the proposed design for the new children’s hospital in Dublin - Leaving Cert DCG - Question A-1 - 2018

Question A-1

The 3D graphic below shows the proposed design for the new children’s hospital in Dublin. It consists of an ellipse and two inner circular arcs. The drawing on t... show full transcript

Worked Solution & Example Answer:The 3D graphic below shows the proposed design for the new children’s hospital in Dublin - Leaving Cert DCG - Question A-1 - 2018

Step 1

Locate the remaining points on the ellipse and draw the curve.

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Answer

To locate the remaining points on the ellipse, use the major radius (a) and minor radius (b) values. The equation of the ellipse is given by: $rac{x^2}{a^2} + rac{y^2}{b^2} = 1$ Determine several key points on the ellipse by calculating values of x and y using this equation. For example:

When $x=0$ , find $y = $ , the endpoints of the minor axis.
When $y=0$ , find $x = a$ , the endpoints of the major axis.

Draw the curve of the ellipse through these points using a smooth arc to represent the shape accurately.

Step 2

Locate the focal points of the ellipse.

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Answer

The focal points (F) of the ellipse can be determined using the formula: $c = ext{sqrt}(a^2 - b^2)$ where $c$ is the distance from the center to each focus. Once $c$ is calculated, the focal points are located at $(±c, 0)$ relative to the center of the ellipse.

Step 3

Locate the centre point for the lower arc and complete the drawing.

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Answer

To locate the centre point for the lower circular arc, determine the radius $R$ of the inner circular arcs. The centre point lies directly below the centre of the ellipse at a distance equal to the radius. Draw this arc using the previously defined centre point and radius. Ensure the arc smoothly connects to the endpoints of the ellipse for a coherent design.

The 3D graphic below shows the proposed design for the new children’s hospital in Dublin - Leaving Cert DCG - Question A-1 - 2018

Worked Solution & Example Answer:The 3D graphic below shows the proposed design for the new children’s hospital in Dublin - Leaving Cert DCG - Question A-1 - 2018

Locate the remaining points on the ellipse and draw the curve.

Locate the focal points of the ellipse.

Locate the centre point for the lower arc and complete the drawing.

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