Calendar: 1869-1870 Page 567

THE SCHOOL 569 and IT are the foci of an ellipse and Ρ is point in the curve find the locus of the centre of the circle inscribed in the triangle SPH Find and Β from the equations sin sin Β cos Β sin sin Β cos' 10 Find the polar equation to the chord of parabolic arc and deduce from it that of the tangent 11 From an external point OPQ Opq are drawn cutting the ellipse in PQqp if circle can be described about PQqp show that OQ and Oq make equal angles with the major axis 12 Find the centre and area of the ellipse a2x2 abxy b2y2 ab by ax 13 If sin χ sin -f sin Zx &c to infinity tany cos 14 If θ be small so that powers above Θ3 may be neglected and if sin θ Αθ ΒΘ3 find Β in terms of from the equa- tion sin θ sin cos find also 13 TP and TQ are tangents la an ellipse the chord PQ is produced to meet the directrices in and show that RP rP BQ rQ TP2 IQ2 16 The locus of the centre of circle which always touches two other given circles is an hyperbola II £udxO airt algebra If χ V3 V- s1 ow that י ג is unity If the number of combinations of η things taken ρ together be equal to the number taken ρ together find Find the number of permutations of the letters in the word Transubstantiation taken two together