Does anyone know the answer the 1988 conics question. Question 5 it is. It is referenced in the syllabus.
I think I am getting it wrong because I keep getting the locus is xy = 16.
The hyperbola H has equation xy = 16.
(a) Sketch this hyperbola and indicate on your diagram the positions and coordinates
of all points at which the curve intersects the axes of symmetry.
(b) P(4p, ), where p > 0, and Q(4q, ), where q > 0, are two distinct arbitrary
points on H. Find the equation of the chord PQ.
(c) Prove that the equation of the tangent at P is x + p2y = 8p.
(d) The tangents at P and Q intersect at T. Find the coordinates of T.
(e) The chord PQ produced passes through the point N(0, 8).
(i) Find the equation of the locus of T.
(ii) Give a geometrical description of this locus.
This is the question.
Cheers for help.
I think I am getting it wrong because I keep getting the locus is xy = 16.
The hyperbola H has equation xy = 16.
(a) Sketch this hyperbola and indicate on your diagram the positions and coordinates
of all points at which the curve intersects the axes of symmetry.
(b) P(4p, ), where p > 0, and Q(4q, ), where q > 0, are two distinct arbitrary
points on H. Find the equation of the chord PQ.
(c) Prove that the equation of the tangent at P is x + p2y = 8p.
(d) The tangents at P and Q intersect at T. Find the coordinates of T.
(e) The chord PQ produced passes through the point N(0, 8).
(i) Find the equation of the locus of T.
(ii) Give a geometrical description of this locus.
This is the question.
Cheers for help.