Calendar: 1873-1874 Page 550

550 GENERAL LITERATURE AND SCIENCE 13 Find the equation to the Ellipse with the vettex as origin If the vertex and nearer focus remain fixed while the centre moves in the line joining them to an infinite distance the curve will become parabola 14 The circle described from an extremity of the minor axis of an ellipse with radius equal to the distance of either directrix from the centre will touch the ellipse in two points one point or not at all as the eccentricity is greater than equal to or less than -ί- 15 The area of any parallelogram that touches an ellipse at the ends of conjugate diameters is equal to the area of the rectangle which touches the ellipse at the ends of the axes 16 Find the equation to the hyperbola referred to the asymptotes as axes 17 If PSp be any straight line drawn through the focus א of conic section meeting the curve in Ρ and and SL be the semi-latus rectum then SP SL and Sp are in harmonic propor- tion 18 The general equation of the second degree οι' xy cy2 -f- dx ey j-f represents with certain exceptions an ellipse or hyperbola according as b2 or 4ac What curve is represented by the equation 2xy 3x 2y 41 Find its axes and position VII -J3Iauc anU J&pijtrital Crigonomttri Show that sin 180 sin and cos 180 cos where is greater than 180 and less than 270 Also trace the changes in the sign and magnitude of sin cos as varies from to 360