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The graphic below shows the logo for the Ladies Professional Golf Association - Leaving Cert DCG - Question A-2 - 2017
Question A-2
The graphic below shows the logo for the Ladies Professional Golf Association. It contains a combination of geometric curves depicting a female golfer. The main curv... show full transcript
Worked Solution & Example Answer:The graphic below shows the logo for the Ladies Professional Golf Association - Leaving Cert DCG - Question A-2 - 2017
Step 1
Locate the vertex and draw a portion of the parabola.
Answer
To locate the vertex of the parabola, we can use the standard form of the parabola equation. Given that the directrix is horizontal and lies at a distance 'd' below the vertex, let’s assume the vertex is at the origin (0, 0) and the directrix is at y = -d.
The focus F would then be directly above the vertex at (0, d). From the directrix and focus, the equation of the parabola can be written as:
y = rac{1}{4p} x^2
where p is the distance from the vertex to the focus.
To draw the portion of the parabola, plot this equation for various values of x to get the curve.
Step 2
Locate a point P on the curve which is 30mm from the directrix and construct a normal to the curve at point P.
Answer
To find point P on the parabola that is 30mm from the directrix, calculate the y-coordinate of P. Since the directrix is at y = -d, point P will be at:
Substituting into the parabola's equation, you can find the corresponding x-coordinate. Once point P is located, determine the slope of the tangent line at point P and use it to find the slope of the normal line, which is the negative reciprocal of the tangent slope.
Finally, using point-slope form, construct the normal line equation: