Calendar: 1865-1866 Page 535

GENERAL LITERATURE AND SCIENCE 537 angles contained by their segments are in the ratio of the para- meters of the diameters which bisect the chords The chord of curvature at point Ρ of parabola drawn parallel to the axis ί8ρ 10 If from the foci S' of an ellipse ST ST' he drawn at right angles to the tangent at then JTand Y' are in the circum- ference of circle on the major axis and ST SY' Β C2 11 If CP and CO he conjugate diameters andPPbe drawn at right angles to CD meeting CA in then PF Ρ θ BCK 12 Two ellipses have common focus and equal major axes Show that there are only two points of intersection and find them 13 Find the equation to the parabola the axes being any diameter and the tangent to the point where the diameter meets the curve 14 Find the equation to the hyperbola referred to the asymp- totes as axes 15 If be point in rectangular hyperbola PC ρ dia- meter show that Qp and QP are equally inclined to the two asymptotes 16 Two equal rods AB BC are connected by hinge at and the extremity is fixed while the extremity is made to traverse Find the locus of fixed point Ρ in Β JUNIOR SCHOLARSHIP -Cuclttr an& risonomrtrj Find the difference between the circular measures of 2g 4' French and of 506 "9 English If sin η sin and tan tan show that must be greater than and less than Prove sin sin cos Β sin cos and Β -Β sin sin Β sin cos --3--