Calendar: 1864-1865 Page 546

548 GENERAL LITERATURE AND SCIENCE In an ellipse tan PSH PHS tan 10 Find the equation to the ellipse the axes being con- jugate diameters 11 CP and CD are conjugate semi-diameters of an ellipse CQ is perpendicular to Ρ Β find the locus of 12 What is the curve defined by -f Find the equation to its tangent 13 Find the equation to the hyperbola the asymptotes being axes If the ordinate MQ of an hyperbola be produced to so that MQ SP find the locus of 14 Show that the locus of the centre of the normal to any point in an ellipse is another ellipse of which the eccentricity is '4g Sa'i' -f- 2a2 ts III Stontftriral Com'c ttttonS Jf Ρ Ζ be drawn touching the parabola in and the directrix in PSZ will be right angle The major axis is the longest straight line that can be drawn in an ellipse If from any point Τ exterior of parabola tangents TP TR be drawn and TV parallel to the axis meeting PR in then PV RV If two chords of parabola intersect one another the rectangles contained by their segments are in the ratio of the parameters of the diameters which bisect the chords The chord of the circle of curvature parallel to the axis of the parabola SP The radius of curvature at the point Jj mm twice the normal The focus and directrix of an ellipse being given find any number of points on the curve