Calendar: 1855-1856 Page 369

GENERAL LITERATURE AND SCIENCE 3G5 cos χ χ 7r 4' IntpSrate cob fr0m t0 י Find the equation to the rectangular hyperbola between the asymptotes and also that of its evolute Trace the curve -f x2 y2 a2 x2 y2 find its points of contrary flexure and the area between the curve and its asymptote semicircle and ellipse have the same diameter Β and centre QPiVis common ordinate QT Ρ are two tan- gents intersecting in find when the angle Τ Β is greatest and the value of CΝ when Find the area of the curve defined by the equation- χ -- between the limits of χ and χ An ellipse and hyperbola that have the same centre and foci will cut one another at right angles 10 cylinder is cut by plane making an angle of 30 with the axis find the dimensions and form of the section 11 If be the radius of curvature to an ellipse and Θ the angle the normal makes with the major axis then a2 b2 a2cos 2sin 20 12 The tangents at the extremity of any focal chord of an ellipse intersect in the directrix and the line joining their inter- section with the focus is perpendicular to the chord 13 The surface of paraboloid the height of which is SA is to that of the hemisphere of the same altitude 16 14 If ζ φ show that χ2 dxl dy2' III-Cijc dTtftccntl Ccntun tn Cuginirti anK dfraiur The questions upon this subject were the same as those set for the Senior Classical Scholarship See ante 355