Calendar: 1869-1870 Page 513

GfiNfiftAfe £JTSRAtOR& ΑΚΪ S0JHNCE 515 TRe equation to conic section round the focus being j2 ן show that the eccentricity H2 Pairs of tangents to parahola intersect in point find its locus when the difference between the tangents of the angles which the tangents make with the axis of χ is constant Find the radius of the circle of which the equation is a5 xy 19x VIy given line BC slides between two lines AB AO given in position find the locus of point from which the lines Ρ Β and PC make the PBA PCA of constant magnitude The circle described- en HP in the ellipse touches the circle on the major axis The tangent to any point Ρ in an ellipse intersects the nearer directrix HK'm show that BT tan PHS is constant If NPQhe the ordinate of an ellips and-thte circle on the axis major find the locus of the intersection of SP and CQ If be the inclination of chord of parabola to the axes and θ and φ those of the tangents at its ends then cot cot θ eot φ 10 Find the equation to the normal of the rectangular hyper- bolaary dl at the point ac -j and' show that the coordinates of the point where this normal again meets the curve are ΧΊΠ -Utffewnttal an integral Calcului Fisb from first principles the differential coefficients of axm a" leg χ and tan Find the different coefficients of sin and of 2" whence deduce that of sin ten Prove that the differential coefficients of Α '1 יי