Calendar: 1899-1900 Page 772

cxx FACULTY of science Shew that of all pairs of conjugate diameters in an ellipse the equiconjugates include the least angle If the centroid of triangle circumscribed to an ellipse lies at the centre the difference of the eccentric angles of 27Γ any two points of contact is Shew that the axes of the conic ax2 2kxy by2 are x2 y2 xy Find the centre axes and simplest equation of x2 y2 Sxy 8x 6y Interpret the equations kS JcLM JcL2 where are conies and Μ straight lines If from fixed point any two lines OPQ ORS are drawn cutting fixed conic in PQRS1 then the polar of with respect to all conies which can be drawn through PQRS is the same Find the length of the perpendicular from the point αβγ upon the line ζ ύ η Shew that the locus of point which is equidistant from three given points is line perpendicular to the plane in which the points lie Shew that if I2m2n2 hm3n3 are he direction cosines of three lines mutually at right angles then the points alv bmv cn etc etc are the extremities of conju- gate diameters of x2 a2 y2 b2 zl c2 -1 Shew that the centroid of the triangle formed by joining the ends of three conjugate diameters is on the diameter conjugate to the plane of the triangle 10 Shew that the lines ax bz ax where form one system of generators of the surface yz zx xy and find the other system