Calendar: 1877-1878 Page 594

592 GENERAL LITERATURE AND SCIENCE 10 If hxy 19' represent hyperbola shew that the equation to tbe conjugate is ab A2 2hxy bf Ify αβ bg 2fgb 11 Prove that any two points and the extremities of their polars with respect to any conic lie on the circumference of another conic 12 Find the cosine of the angle between two straightlines in terms of the direction cosines of the lines Find the direction cosines of tbe shortest distance between tbe lines Jf β η χ a' β ζ γ' I' m' n' 13 Find the locus of the middle points of the chords of the surface aj2 bf bz" 2dyz 2exz 2fxy which are parallel to y- η 14 Prove that the reciprocal polar of any circle with regard to given circle is conic and when the conic is hyperbola find iis asymptotes and axes 15 Prove Pascal's theorem that the intersections of the opposite sides of any hexagon inscribed in conic are in straight line 'J Reciprocate this theorem XX -Qtffmnttal anU integral Caltulus Find the differential coefficients of χ tan-1 tan 4s and log sinj 10g SJ