Calendar: 1871-1872 Page 527

GENERAL LITERATURE AND SCIENCE 527 -analptital eomttrp Obtain- the distance between two points in terms of their polar co-ordinates and deduce the polar equation to the circle The sides of parallelogram are given in magnitude and one side is fixed As the other sides move what is the locus of the intersection of the diagonals Prove that the circles x2 6y -f 16 touch one another and find the equations ot their common tangents Find the polar equation to the tangent to the conic r- cos θ at the point for which β and thence show that the angle subtended at one of the foci by the part of the tangent inter- cepted between two fixed tangents is constant parabola whose axis passes through the centre of given ellipse and whose latus rectum is of its minor axis touches the ellipse of the extremity of the minor axis Find the equation of the parabola and that of the chord of intersection of the two curves If two diameters of conic be such that one of them bisects all chords parallel to the other then the second will bisect at chords parallel to the first On each side of triangle an equilateral triangle is described externally Find in trilinear co-ordinates the equations to the three lines joining each vertex of the triangle to the vertex of the opposite equilateral triangle and show that they all meet in point Find the equation to the tangent at any point of conic either in trilinear or Cartesian co-ordinates also the equation to the polar of any point Define the anharmonic ratio of range and show that if pencil be cut by any transversal the anharmonic ratio of the range is constant