01 May Question 1 (4 marks)In GeoGebra, Cabri Geometry or otherwise, construct and label triangles ABC and ABD with
Question 1 (4 marks)
In GeoGebra, Cabri Geometry or otherwise, construct and label triangles ABC and ABD with
common side AB. Find and label the centroids G, H in these triangles.
You may conveniently choose coordinates for A,B,C,D, and extract the coordinates for G and
H from there, so long as ??????? and ??????? are not similar/congruent.
Show visually that ???? ? ????, and verify this by showing that GH and CD have the same
slope. You do not need to find the Cartesian equations of GH and CD.
Question 2 (10 marks)
(a) Find the centre and radius of the circle with equation ??
2 + ??
2 + 3?? – 6?? = 0.
(b) Find the equation of the normal to this circle in part (a) at (0, 6).
(c) Determine where this circle from part(a) meets the circle ??
2 + ??
2 – ?? – 4?? = 12.
Question 3 (6 marks)
A parabola is given by ??
2 = 4????. P and Q are points on the parabola and ????¯¯¯¯ is a focal
chord. If ????? is the tangent at Q and ????? is parallel to the axis of symmetry of the parabola,
show the locus of this point T* is given by (?? + 2??)??
2 + 4??
3 = 0.
*T will vary as you vary P and Q. The locus of T represents the trajectory of T as we change P
and Q.
Verify the above by choosing a value of ?? ?
1
4
, P, and Q, and include a diagram showing the
parabola, P, Q, the consequential coordinates of T, as well as the locus of T.
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