Calendar: 1875-1876 Page 573

GENERAL LITERATURE AND SCIENCE 569 Find the angle between the two straight lines Ax2 Bxy Cy2 Prove that the locus of the poles of all chords of an ellipse which subtend right angle at the centre is concentric ellipse Investigate the polar equation of conic referred to the ocus as pole and the polar equation of the tangent at given point circle touches the conic 4- cos at the point where ד and passes through the pole prove that the two points of inter- section with the conic lie on the straight line -j- 2ecos e2 e3 cos6 -f e2 cos Θ and that this chord touches similar conic having the same focus and its centre at the intersection of the directrix with the axis Find the general equation to the conic which touches the rectangular axes at given points What is the condition that the conic may be parabola If the chord of contact has always constant length the locus of the vertex of the parabola is 10 An ellipse whose semi-axes are slides between two rectangular axes shew that its foci trace out the curve whose equation is χψ -j- 4β2 11 Express the distance between two points in space in terms of their coordinates rectilinear or polar Find the volume of tetrahedron the rectangular coordinates of its four angular points being given 12 Find the condit on of perpendicularity of two straight lines whose equations are given and prove that the two straight lines represented by the equations ax by cz Ix2 my2 112