The image below shows the parabolic bridge at Mizen Head in Cork - Leaving Cert DCG - Question A-2 - 2022
Question A-2
The image below shows the parabolic bridge at Mizen Head in Cork.
The drawing below shows the axis AA₁, focus F, and two points P and Q on a similar parabola.
(a) L... show full transcript
Worked Solution & Example Answer:The image below shows the parabolic bridge at Mizen Head in Cork - Leaving Cert DCG - Question A-2 - 2022
Step 1
Locate the directrix and draw directrix
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To locate the directrix, draw a line parallel to the axis of the parabola, positioned at a distance equal to the focus distance from the vertex. Label this line as D, which represents the directrix.
Step 2
Location of vertex
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The vertex (V) of the parabola is located at the midpoint between the focus (F) and the directrix (D). Mark and label this point as V.
Step 3
Location of points on and above latus rectum
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Identify the latus rectum, which is a line segment perpendicular to the axis of the parabola passing through the focus. Mark points above and on the latus rectum at equal distances from the vertex and label them A₁ and A₂.
Step 4
Location of points below latus rectum
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Similarly, mark additional points below the latus rectum extending downwards from the latus rectum line, and label these points as B₁ and B₂.
Step 5
Draw curve (Any = 1)
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Using a smooth curve, connect the points located above and below the latus rectum. The resulting shape will represent a parabola, ensuring that it passes through the given points P and Q.
Step 6
Draw a tangent to the curve at point Q
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To draw the tangent at point Q, first, determine the slope of the parabola at that point. Use the derivative of the parabola's equation at point Q to find the slope. Then, draw a straight line through point Q using the determined slope, representing the tangent line.
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