Calendar: 1853-1854 Page 336

832 GENERAL LITERATURE AND SCIENCE Ρ and and making Μ right angle then CB being the semi axis minor MQ AB9 Α Ρ MR li-' rod of given length slides with its extremities in para- bolic groove find the locus of its centre Find- J'χη mx dx between χ and χ 00 cos χ dx cos Pairs of tangents are drawn to an ellipse find the locus of their intersection when the difference of the tangents of the angles they make with the major axis remains the same If equal triangles be described on the same base find the locus of the intersection of perpendiculars from the extremities of the base upon the sides If Ρ be normal to an ellipse at right angles to SP Ρ Ν an ordinate show that Ρ 10 Find the surface of an oblate spheroid and deduce from the expression the surface of sphere -χ 11 Trace the curve defined by y1 or jt- and find its χ area and find the asymptotes rectilinear and hyperbolic in χ a2 χ 12 Find the radius of curvature when the arc is the indepen- dent variable Ex 2cx 2cy λ ea- gin 13 Find the length and coordinates of the extremity of the perpendicular from given point upon line 14 Find the equation to the hyperboloid of two sheets show that it has an exterior conical asymptote draw tangent plane to it and find the length of the perpendicular from the origin upon it