Calendar: 1867-1868 Page 486

GENERAL LITERATURE AND SCIENCE 487 10 If CP and CQ be semi-conjugate diameters of an ellipse find the coordinates of in terms of those of and show that CP1 CI CA' C52 11 From the origin two lines OC and OB are drawn perpendiculars to the two straight lines 4-1- ί ϋ-2 then area Qg a' β2 42 12 Find the equation to the tangent to an ellipse and the length of the perpendicular from the focus on it 13 The tangents drawn at the extremities of any focal chord of an ellipse will intersect in the directrix and the line from this point to the focus will be perpendicular to the focal chord 14 If CP and CQ be conjugate diameters of an ellipse and an equilateral triangle PRQ be formed on PQ find the equation to the curve traced by Jt 15 Show that Jy j3 the equation to parabola and deduce from it the equation to its tangent 16 The tangent to any point of an hyperbola being produced to meet the asymptotes show that the triangle cut off is of constant area 17 cone is cut by plane the section made by the cutting plane with the original triangle being parallel to the slant side show that the boundary of the section of the cone is parabola and find its latus sectum Division IV-Siffeunttal anU integral Calculus The tangent to any point in cycloid is parallel to the corresponding chord of the generating circle Expand log -f- sin according to the powers of and sin-1 according to the powers of