Question 1
(1) (a) Draw an ellipse with major axis 120 and the minor axis 70 using the concenric circles method.
(b) Construct a normal and a tangent at a point P on the ellipse 45o from the centre of the ellipse and at the right side above the horizontal axis.
(c) Construct an involute for one complete revolution on an equilateral triangle of side 55.
Question 1A
The candidates were given the major and minor axes and were required to draw an ellipse using the concentric circles method. The solution to this question requires that the candidates draw concentric circles using the major and minor axes as diameters, and then divide the circles into 8/12 equal parts. To locate the points for drawing the ellipse vertical and horizontal lines are drawn from the big and small circles respectively.
Question 1B
This question requires that a point of tangency P is located on the ellipse, and on the point a normal and a tangent is constructed. To solve this, one must locate the local points which are done by using half the major axis as radius and describing arcs on the major axis with the minor axis as the centre.
Question 1C
This is a question that has to do with drawing an involute to an equilateral triangle.
Observation
Question 1A
Candidates were to construct a common interior tangent to the given circles.
This question was attempted by many of the candidate but very few got it right.
Many of the candidates could not follow the process of locating the points of tangency on the circle correctly.
Candidates were expected to do the following:
- COMMON INTERIOR TAGENT
- Draw the centre line ( 1 hori., 2 vert., at 80 apart)
- Draw two circles O 40 at centres F and G
- Bisect FG to locate point H
- Bisect FH to locate point J
- Drawing a semicircle with centre J on FH to locate point K on the circle with centre F
- Locate point L on circle centre G using radius KH at centre H
- Draw the interior tangent on KL extended at both ends.
The solution is shown below:
Question 1B
This question is on tangency. It requires candidates to work from to kwon points and locate the tangents. Most of the candidates who attempted this question did not get it right.
Candidates were expected to;
- A PAIR OF PLIERS (TANGENCY)
The solution is shown below:
