Question 2
An ellipse has a major axis 120 long and its foci are 80 apart.
(a) (i) Construct the ellipse.
(ii) Measure and state the length of the minor axis.
(b) Draw a tangent and normal to the curve at a point P above the
major axis and 35 to the right of the minor axis.
Observation
The question involves the construction of an ellipse. Candidates were required to first establish the minor axis before constructing the ellipse.
Some of the candidates who attempted this got it wrong.
Candidates were expected to:
(A) DRAW THE ELLIPSE
(i) draw the major axis;
(ii) locate the foci points, 80 apart;
(iii) draw the minor axis, using half the major axis as radius from F1;
(iv) locate points of curve using any appropriate method;
(v) join the points into a smooth curve;
(vi) state the length of minor axis.
(B) CONSTRUCT THE TANGENT AND NORMAL
(i) locate the point of tangency;
(ii) join the foci to the points of tangency;
(iii) bisect angle F1 P F2 to obtain the normal;
(iv) draw perpendicular at P to the normal for the tangent;
(v) draw neatly.
The solution is shown below:
CONSTRUCTION OF ELLIPSE, TANGENT AND NORMAL